Sheet music will not give players the absolutely exact instructions for playing a piece - if it says get faster, slower, louder, softer or whatever, it's not (usually) going to say exactly how faster or louder etc. It's also not going to tell each string player precisely how loud they need to play to be heard properly above to the brass section.

It'd be generally a bit unreasonable to expect musicians to follow such instructions, as they deal more will relative precision than absolute precision i.e. matching a beat you see/hear, no problem, picking out 144bpm at 50db with no reference, good luck.

Those things can be largely a matter of personal taste and expression, and dependant on the characteristics of the venue or ensemble anyway. It just matters that the group as a whole is making coherent decisions - how much faster can be discretion as long as everyone gets just as fast.

So you kinda need one person with an ear on the whole piece, centrally controlling those variables. With a smaller ensemble you might get away nominating a player to do it, or each player using their own discretion. But with a bigger group that's going to be difficult.

Also worth noting that for a big enough group or stage, the time lag (limited by the speed of sound) of sounds from one side of the stage reaching another can have a perceivable effect. A central visual cue gives everyone a common time to work off.