With normal conventional weapons the general expectation is to hear but not see the rounds being fired at you.

With the arch-typical science fiction setting, you would expect to both hear and see an energy weapon being fired - like in Star Wars for instance. So you could trace the fire back to its source easily. This is pretty much the standard for science fiction shooters.

What if there was a game where you could see, but not hear the weapon being fired. You could see whats firing it, but no you wouldn't hear it. This goes against what you would normally expect, so how would you feel about it?

Taking this concept even further, what about a game where you could neither see nor hear a weapon being fired at you, only notice the effects on the environment with a miss or on yourself with a hit. So how would you feel about it?

To me its an interesting concept, its the difference between what is expected and what you experience that may cause problems for some peoples enjoyment of a game like that. I don't know whether or not I would like the idea, I guess it depends on the setting eh? 

That game would be very sniper-heavy. I hate snipers. Ergo, I'd hate that game.

Isn't that the same for sound only games?? So unplayable for us but playable for blind people..
So for a deaf person it's probably playable.. but I won't like it.. the deaf person will whop my ass in that game...

Its more like realism taken to the extreme level. I realistic gun makes a lot of noise, a realistic gun with a silencer makes very little noise and a realistic energy weapon makes no noise.

So like...lasers that actually travel near the speed of light? Yeah, that wouldn't be very entertaining.

Realism can be no fun. No respawning, no regenrating health, no more run-and-gunning, no more running at a constant 20 mph...and if adding too much realism detracts from the fun experience, then realism must go.

Yea thats true, but it would be a cool implementation for some kind of slow charge silent weapon that you can either Snipe with or creep around and get people in the back with. Like the spy from TF2.

It would be a refreshing change, though.

Instead of playing as a roided-up super soldier version of Arnold Schwarzenegger or even an almost-human fighter with haxx0r combat gear, you could play as an somewhat above-average soldier with human strengths and weaknesses. Add a need for tactics, planning, wounding and other assorted stuff and you have a somewhat realistic, "thinking mans" FPS - not exactly the easiest thing to design and program, probably wouldn't sell much, but I'd sure as hell play it.

Soundless weapons would instill quite a bit of paranoia in the players. I like it. :p

no one cares -_-

Well, I've got some good news for you. You can download this for free, assuming you haven't played it since its 2002 release.

It sounds nice in theory to play as an average Joe on a real battlefield, and in fairness it's not that bad of a game, but America's Army just isn't as much fun (to me) as other FPSs simply because it is realistic, and lots of others agree. As an aside, it does meet your criteria of being a more cerebral game than most, although the necessity for team tactics means that once someone plays Rambo your whole team suffers.