like a phaser, or indeed any light-based weapon
To be sure, nobody has said that phasers would be light-based. (That is, except unreal people from an alternate universe where Trek is a TV show.)
And clearly they are not, for the above reason. If it meows like a cat, walks like a cat, and refuses to swim, what possible point would there be in calling it a duck?
Although the weapons in "The Cage" were called lasers, real-life lasers don't function like that at all.
The ones I use do. A red beam that melts the things it hits is pretty laserlike behavior - and the early TOS VFX actually gives us faster beams than the more refined TNG stuff, so that part is okay as well (although it would also be okay to say that it takes a while before the beam ionizes enough of the air around it to create the bulk of that glow).
oddities like "time warp" that makes the ship translucent, Pike's bulky TV, Pike's blatant bigotry and a little paper printer on the bridge.
These may be "odd", but they are by no means aberrations from the Trek norm. Many characters have been "bigots" if you by that mean that they are misogynes; paper prints reappear in TNG; and bulky items from the past are treasured by virtually each and every one of our heroic starship captains. And there's no reason to think that the ship would become translucent for her crew; none of them react as if it did. It's just artistic license if we take it that way. (The crew does appear to suffer from excessive noise during "time warp factor seven", tho, as we get hand signals but little or no dialogue. But there's always increased noise on the bridge during high warp in TOS, too. For whatever odd reason.)
As for controlling a phaser with just three buttons, I can control entire kingdoms with two plus a handy but not necessary thumbwheel... More buttons would just mean more finger movements, translating to more opportunities for an epic fumble.
Timo Saloniemi