Acceleration should be cut to at most 1/4 of where it is now, imho. It should be for going in a long, straight line only. Otherwise (as others has indicated) it obviates a large number of other mechanics.
That wouldn't solve the problem. Acceleration is already slow and annoying. It's slow enough to where if you get caught with s-burn off, turning it on wont save you. You need to e burn to get enough distance to safely engage s burn.
It's when the player is up to speed (for free) that it breaks some other things, like being able to easily catch other fleets you shouldn't.
I'm not sure increasing the cost would solve the issue either. Fuel burn is already expensive enough that if it cost any more I wouldn't ever use it.
I think the only solution is to have enemy fleets using it as often as the player, or remove it entirely, and personally Id hate to see it go because it's a nice quality of life feature.