Yes, every lens gets one as soon as I get the lens. If it's a used lens, I do a detailed cleaning. They are never removed.
Neutral would be more of a neutral density filter, used to reduce light, so what you are asking about, aren't neutral filters.
You might choose a Skylight 1A, or 1B (supposed to be warmer) or UV (all of these are called Haze filters), which are supposed to reduce haze.
All you need is to have one lens ruined by a stone, or bumping, and you'll always buy a protective filter.
Also, if I'm shooting and there's mist or dust (I confess it's wrong, but it's the truth) I wipe the filter with the corner of my shirt, a tissue or a towel, and don't have to worry about ruining a lens.
What would you do if you got a speck of something directly on your front element and you were shooting sports, or an event? Doesn't matter, if you are shooting a still life. Stop... go get a little lens tissue out of the sealed envelope and maybe some liquid, then go to a dust free place. You don't want to scratch the lens, or make it worse. Blow it off with the bulb and carefully clean the lens? Then go back to shooting.
Or wipe it off with your shirt?
You can save $39 and skip the filter to protect your $400 to $2000 lens.
Does that make any sense at all?
Consider the filter a small inexpensive, lens insurance policy.