I've always felt that in the game's current state, the correct course of action is to incentivize pushing quickly, as opposed to penalizing teams that take a while. As it is, if ubers are even and players on both teams have respawned, the cap usually marks the beginning of a stalemate. The attacking team will usually not be as healthy as the defenders, or will have to leave a player behind to finish the cap if they want to be aggressive. Trying to use the stick approach to keeping teams from stalemating means teams would be forced to take bad fights frequently, or potentially even cause more stalemates if waiting grants one side an advantage. Instead, you could encourage them to move by offering some kind of diminishing combat bonus to the cap itself. Overheals could be an easy, already in-game example of what I'm talking about: If capping a point granted an extra 25% health that drained at the same rate as an overheal (so, best case, you'd have soldiers with 350 health for a few seconds), the attackers would be more likely to just keep moving as quickly as possible into the defenders. It would additionally make fights much more conclusive, since a defending team is less likely to retreat and attempt to stalemate the next point after losing a small advantage if the attackers gain something from capping.
It doesn't totally eliminate stalemates (which I don't think should be the goal anyway; just to reduce their frequency). If losing a point grants the other team a sizable advantage, you could be less willing to do anything at all if your health ad does drain away. But I do think it makes stalemates less likely, and it also makes a team that wins mid much more likely to take it all the way to last. As long as teams are scoring, or one team holds a round advantage over the other, there will always be a towering incentive for the other team to push, no matter the cost.
also theres a fuckton of other ways to implement this that change the game in different ways, from just boosting the overheal cap, damage bonuses, all the way to granting a bonus just by touching the cap, or just bonusing the people who are actually standing on the thing. the point is that i think the solution lies in incentivizing pushing instead of pissing on people for stalemating