Two words: Already Happened.
Power Creep from 2nd edition to now has already taken every Expert Class, every Priest Class, and every Mage class far and above where they were. At this point, preventing warriors from getting a buff isn't preventing power creep, it is preventing game balance because everything else has already crept up.
Might work... unless they find a way to do it at range. Like with the Longbow that has the slow ability currently listed. Then you have just created a lesser version of the same problem, unless it is Battlemasters, then it is just the exact same problem.
Or you incentivize multi-classing to get two levels of rogue, for bonus action disengage, then you can do it in melee as well. Or get the mobile feat.
So... the martial slowing ability stacking would actually just create the exact same problem, just with a little more work having to be put into utilizing it.
Declaring it before is rather pointless, if it is at-will like it should be. Because at that point you just declare it for every single attack. And no, they should not be instead of damage. That would be a terrible design, as discussed previously. Pushing an enemy 10 ft instead of trying to end the fight is a horrible use of your attack.
And tracking multiple, stacking states would be a nightmare. It isn't so bad if it is one person, against one target, but if you have a full martial party who end up stacking four or five different effects on four to six different enemies? No thank you, that is a recipe for disaster.