You ask some very insightful questions about modeling lights. How important are they? They are very important especially with regard to setting the exact height in the exact placement of your lights. The more experience you have the less critcal the need for modeling lights becomes, at least in basic situations.
As you develop familiarity with your equipment you can get by with no modeling lamps, especially in rather generic lighting situations . But for example let's say we are trying to establish exactly where a reflection falls on a piece of glassware or where the nose Shadow Falls, or where exactly the highlights are placed on a person's eyeball, or more importantly, where the reflection falls on someone's eyeglasses. I used to shoot family portraits every day for 8 hours a day, 5 days a week, and I personally think that modeling lights are the separator between great work and good work. Or between good work and poor work. It's quite easy to slap up a light stand and umbrella and fire away, but let's say you are trying to position a kicker light or a hair light and you want the highlight to be placed "just so". When you have a modeling light the model or portrait sitter can "feel the light" and how it shines upon their eyes and face, and you the photographer can see when a person has moved or turned so that the light is no longer in the ideal placement. Modeling lights come into play in difficult and demanding situations, whereas shooting with speedlights you have no modeling lights and are going upon immediate-but-still-after-the-shot feedback. With modeling lights you are kept apprised of exactly where the light is falling,at every second, before and after the shot, and the subject can feel how the light is hitting them. When you shoot without modeling lamps you are basically shooting based upon experience and review of the images, but at the margins you are prone to falling into making shots in which the light is no longer ideal and its placement is "just okay", as opposed to excellent or optimal.
One might say that modeling lights are a lot like seatbelts. Lots of people do not use them, or whine about them, but when you need them, they're really good to have.
When you are shooting in dark environments people's pupils will become quite wide. I have always been aware of this and have always tried to keep ambient light levels high enough to avoid the cow eye look, but when you're in a dark studio, shooting with speedlight flashes, you will often see really large black eyes, which have very little color, and which look to me like heroin addict eyes or cow eyes-- this is why the Paul C. Buff Einstein monolight has such bright and fully adjustable modeling lamps. People who are expert and demanding at studio lighting look at the eyes as a matter of course, and work that looks good to some people will be unacceptable to demanding clients who are used to seeing photos done by master-level photographers and in high-end publications. These days, and in the past, bright modeling lights in professional level studio flash allowed for easier focusing especially with a view camera stopped down, and of course you can also shoot with the lamps using tungsten based film, or a white balance achieved with a custom setting while shooting either digital video or digital still images.
The other unstated advantage to modeling lamps is the ability to preview your lighting setup in terms of ratio, in a WYSIWYG way. The modeling lamp gives you a visual clue as to how lights interact with one another. Most newer systems use quite a bit of adjustability in terms of flash power and have modeling lamps which proportionally track the power output of the flash, so you can see, literally see, in a WYSIWYG way, the effect of one light in relation to another light based upon what you visually see---- there is no guesswork. This allows you to work quickly and fluidly and to make changes without the need to constantly take flash meter readings or test photos.
One can literally see the effect of a light and the modeling lamp will show you the relative strength of the flash burst you will get when the picture is made, in advance of taking a shot.
When you work with speedlights you have to keep in mind , "Oh, that light's more powerful than that one", as you look at little black boxes and mentally keep track of the power settings.Modeling lamps turn what is a mathematical nightmare into regular everyday seeing.
Bright, powerful modeling lamps can also turn dark interiors and locations into more brightly-lighted places, and you can also pick up a little bit of warmth by using a somewhat slower shutter speed than the maximum synchronization speed.
No, a few flash pops will not cause a person's eyes to constrict, that is not how the human eye works. If you want small pupils, you need to keep the ambient light High and in the past I have used a 75 watt work lamp as a focusing aid, and to keep my subjects out of the dark and with their eyes constricted somewhat. The problem really occurs in the traditional photo studio, in which most extraneous light has been eliminated. It is in this traditional "studio environment" that Speedlight formal portraiture looks so different from work which has been done with modeling lamps. For example, with the top end lights from Speedo ,you have 250 watt quartz lamps, which cause the pupils to be very small. This is seen most often in high-end fashion and lifestyle magazine work, in which you see very small pupils and colorful eyes.
When I see a formal portrait, meaning a studio-type portrait with great big, black eyeballs, I immediately think shoestring budget, speedlights pressed into where they are not the right tool for the job.
We are talking about a specific look. The difference is between an eye which is inviting to look at, and one which looks like a big cow eyeball. If the environment is even relatively bright, people's eyes will look okay. Regarding this black eyeball or cow eye look , I am speaking mostly of dark Studio work, but it can occur on location as well especially in darkish interior settings. One always has to be aware of how people look. Look for lint balls, necklaces out of adjustment, rings turned so that the gemstone is off to the side,shirts unbuttoned, neckties crooked, lapels badly adjusted, shirt collars out of whack, and yes, eyeballs which look like they belong to cave explorers.
I think as I mentioned, the more experience you have the more you can compensate. But let me tell you this, when I was a working family portrait photographer we used roller base stands, which allowed us to easily move the light through an arc on the floor so that we could determine by visual evidence the exact, best placement of the main light. There is a difference between predicting or estimating and actually moving the light. This ( actually moving the light and evaluating its placement in real time) is quite a bit different from plopping down a light standand and umbrella and setting it to 20 or 30 degrees to one side or the other of the subject and just firing away.
When you are doing Paramount or modified Loop lighting, one of your biggest concerns is the exact length of the nose shadow, and the angle of said shadow. The shadow should be close to but not touching the upper lip of the subject. When you actually take the time to set the main light's height and angle, before the shot is made, your photos will be better,or maybe tremendously better. If however you just plop down a light on a stand and set a rough angle you will have to work out the details based upon what you see upon review of your shots. One method is the old school way, and other method is how people who are less than expert shoot when they get their hands on some studio lighting gear.
People who whine about the brightness of modeling lamps are typically not in front of the camera very often. Models, even amateur models, have developed or should develop a sense of finding and feeling the light. This is perhaps the biggest thing you can help your subjects with, especially if they have aspirations of becoming a model; they need to learn how to sense when the light is hitting their face in an attractive way, and modeling lamps help do this. You can literally _see the effects_ of your lights upon your subjects as they are move about the shooting area.The word modeling lamp is in itself a clue as to what the lights are there for.
Modeling lamps show you both how the light models the features of the subject and they let models understand how to interact with said light. The fact that you have seen people who turn off the lights does not mean that the lights have no value, but that the people who were using lights do not fully understand what the lights are designed to do, or that at certain times there is much value in having additional light besides what is ambient.