Aelkyr5CP in TF2 does have this problem : there's just no real incentive for a team in the lead to push since they're already winning.
As long as one team has an incentive to fight, the other team has to meet them or concede ground. The team that is behind has the incentive to push since they will lose if they don't. The only time a stalemate should occur is when neither team has the reward outweighing the risk. In reality things people call "stalemates" occur for a couple reasons, mostly due to players having poor strategy and not playing enough.
People say a stalemate is being done because players aren't doing anything for 2-3 minutes after winning mid and sitting on enemy last. This is usually because the team is scouting out information and is deciding what to do. What hold does the enemy have? Where is sniper watching? Where is gun? Where is medic holding? Do we want to offclass? These questions are either answered inefficiently (because players do not know what they are doing and don't start doing it soon enough e.g. spamming the gun as it is going up) or the team isn't practiced enough as a unit to know where they have to be to support a play since they haven't put time into it. In reality, you could already be doing things like setting up and doing a sac within 60 seconds, but because teams aren't properly practiced (likely due to lack of time investment since this is a hobby, not our lives) there will be some players who need to be told where to go and then go there instead of being in the position already.
Better players are usually ready to do things and support others, worse players generally have to have the team play around them and they play their own game. It's why when you get to a higher level, players are more selfless and move as a unit than at a lower level where people are split and doing their own thing. This is why you see better teams stalemating less on broadcasts and why the common thing people call a stalemate isn't really one. One team is just taking all the time they can to make the best play possible. Reducing the round timer forces people to make a decision faster if they want to attempt more plays, but a team could also decide to take all the time they can and make an informed decision for one good play which they may deem to have a higher chance of success.
To look at some numbers if anyone isn't familiar with probabilities, 2x40% plays has a 64% chance to work once, whereas an informed 1x70% chance play has the 70% chance to work once. What is actually better is up to the teams and players, not up to the round timer. Even now, it is likely more efficient to constantly try for the lower % play as you have more shots at it with a longer round timer than only a couple shots at a set up play. If you go for 5x40% plays, it has about a 92% chance to work whereas 2x70% plays has about 91%. These numbers are arbitary and most teams would do a combination of them where they set up a longer play but then instantly execute a quick play if they see the opportunity.
A final point on stalemates is that if you truly want to reduce them, then you need to look at what actually causes them. Reducing round timer doesn't really change anything other than require more decisive shotcalling to do slower plays. It's mostly just placebo of players thinking they need to move faster and take more risks because the timer is lower. Nothing new has openend up in terms of strategy other than the points cap themselves after a round reset and ubers reset (which is pretty big if you know what to do with that information). Teams can still stalemate it just means you will get more midfights rather than the dynamic flow throughout the whole map if stalemates were less of a problem.
The things that alter stalemate length are map design, ubercharges, offclasses and some specific unlocks (e.g. vaccinator or quickies). If you want to change stalemates then have to change these things. Reduce the impact of ubers, remove/change class limits, ban/allow unlocks and alter maps in such a way that pushes the solution you want.
A change in ruleset like this isn't going to really alter the gameflow to be any better or worse for players, it will just make watching it more interesting.