Your idea would make it easier stalemate because pussy teams that usually don't ever push without a giant advantage (7) will now literally have zero reason to push at all because they are playing defense. It would just be retards holding last with pyro engi fag setups for x amount of minutes as the other team attempted to break the stalemate by pushing in with uber cover and over.
If anything should be changed it should be the round timer. With a 30 minute time limit you can go up a round or two in the very beginning and then literally sit on the enemy teams fourth point for ~10 minutes doing absolutely nothing and then right before the timer runs out and resets the mid you fail a "push" into last while keeping your medic up and let the other team take their second back. Then rinse and repeat. This is still a problem to a certain extent in ESEA like in second halves when teams have the lead and are less incentivized to push and finish off the game while taking a risk, because they can run out the timer. I feel like in the first half this is almost a non issue (from my experience in ESEA at least), and so long as teams aren't that big tryhards that they will purposefully sit on their dicks and do nothing for 10+ minutes just.to assure they win a game it's good for the most part.