Yes, IMHO, for most people a FF camera IS overkill.
As Keith said, the lens remains the same, it is the Field/angle of view that changes based on the sensor/film size.
What you need to remember is the base/reference point of the camera or the normal lens is different. So you have to reset where your base is.
- APS-C (Canon crop) is 35mm
- FF is 50mm
- 6x6 cm film is 80mm
- 4x5 inch film is 135-150mm
Frankly, the simplest way is to forget FF, and just think APS-C. 35mm = normal/standard lens, 50mm = short tele.
Or magnification; 35mm = 1x, 70mm = 2x, etc.
If you try to convert back and forth between FF and crop, in your head, it is very easy to get confused.
Example. When I work with my 6x6 camera, I reset my brain and think 80mm = standard lens. I do not convert from 6x6 to/from 35mm/FF, as that gets confusing real fast.
First look at the lenses, and see if the lenses available to your T4. And is it adequate for the tasks that you want it to do.
My favorite lens for my Nikon crop camera is the 18-140. The Canon equivalent is the 18-135. This is a great GP lens.
But it is not a fast lens. I consider it a daytime lens. Indoors you need to crank up the ISO a lot, or use a flash.
Note that you will NOT get a FAST and WIDE range zoom. This is an either or situation.
The expensive FF Canon Pro lenses are f/2.8 and f/4, and have a much short zoom range than the 18-135.
Sigma has a few FAST f/1.8 zooms, but the zoom range is even shorter at 2:1, like the 18-35 and 50-100.
For your T4, also consider 3rd party lenses like Sigma, Tamron and Yongnuo.
If you want FAST lens for indoors, it will be a compromise.
#1 - If you want a FAST zoom, there is the Sigma 18-35 f/1.8. It is a short range zoom, stopping at 35mm. But that should be fine indoors, where you are not likely to be zooming in a lot. If you need more reach, you have your 50mm f/1.8.
#2 - A FAST prime is the 35mm f/1.8. The 35mm is a normal lens for Canon crop sensor camera. Canon does not make a crop sensor 35mm lens, only a FF 35mm lens. If you want a crop lens, you need to look at Yongnuo or Sigma.
For my Nikon D7200 (APS-C camera), I have the 18-140 f/3.5-5.6 for a GP lens, and a 35mm f/1.8 for indoor low light photography. But I also shoot more outdoors than indoors. If I shoot indoors, I use a flash.
If the lens you want is not available, then consider FF. Look at the FF lenses.
But realize that FF camera and lenses will be more expensive and heavier than crop camera and lenses.
And you will still not get FAST, WIDE range zooms, because they currently do not exist.
Note, there is no one all purpose camera/lens.
There is a saying "jack of all trades, master of none." And this is true in this case.
In my case I use a DSLR for outdoor or indoor flash.
For family events, I will usually bring my small P&S, as it is easier and faster to use.
The major and serious problem that I have with a P&S, is that there is something called shutter lag. You press the shutter, and a second or two later, the camera finally fires. This is normally not a problem. But it is impossible to track and photograph fast moving kids. They moved 3 feet in that 1 or 2 seconds, and I missed the shot. The DSLR, like your T4 does not have that shutter lag problem.