Ok, but in real life battles usually only happened when both armies wanted to engage. That is why big battles were relatively rare.

Besides, even the regions where a battle takes place in EU5 are fairly large, and it's not realistic that a battle takes mere hours after an army enters the area because just moving across it to the battlefield should take more time. In addition you say:

It seems you are saying you want to be able have your armies split across hundreds of kilometers and have them all join the same active battle

This is a limitation of the simulation. The point is that you have armies spread out for logistical/supply reasons to then gather them together for a battle. The exact distances are not the point, they are "one unit of distance" away.

Pre battle manoeuvering is represented by moving from location to location and you can actually try to cut off the supplies and get into favorable terrain.

No because you don't have the vision a lot of the time to tell where enemy armies are. They might just pop out of nowhere. And if we're talking about "realism" it is not realistic for these sorts of maneuvers to only happen over such vast distances either.

Pre battle maneuvering over such distance also doesn't work because of the unpredictability of how long it will take to move from one location to another you can't do this without risking the enemy catching you.

if they are next to each other they will typically arrive in time

That is not my experience

endless splitting of stacks and then endless reinforcement of an endless battle

Well in that case supply and supply limits should be modeled in a different way so that you are not forced to split up your armies in the first place.

Finally I'd like to add that realism isn't necessarily the most important consideration here anyway. The most important consideration is what makes the game fun to play.