the core problem of 6s has always been stalemating, but it doesn't have anything to do with map or game mode design.
you can make 5cp maps bigger with wider chokes so teams can push into points without using early, except it would make sniper overpowered and projectile classes worse.
you can make attacker spawns closer to capture points or defender spawns farther away so there is less penalty playing aggressively, but now the game snowballs hard and heavily favors the team that wins mid.
you can add a shot clock and enforce it so teams are pressured to push more without addressing WHY the game stalemates, so you'll just frustrate players by forcing them to take uber exchanges they don't want.
the real issue is that the only consistent way to break stalemates is ubercharge. the only real tool you have in this game. setting up sniper/spy or sac plays to break a last hold take way too long and are easy to counter. when those plays don't work the defending team still doesn't have enough of an advantage to push out of last too. that's not going to change because we're past the point of Valve adding new abilities or reworking and rebalancing classes for that.
one problem with ubercharge is that the team that pops first (assuming equal ubers) is already at a disadvantage. who usually has to pop uber first? the aggressive team that ubers through a choke trying to break the stalemate. so stock medigun is responsible for giving defensive teams enough of an advantage to slow the game down when there are equal ubers.
compare that to kritzkrieg on both teams where the team that uses first usually has the upper hand, promoting aggressive play. playing against kritz also might not be as oppressive as playing against stock when your team has uber disadvantage so there could be more room for counterplay. it also charges faster.
I am totally guessing but experimenting with different medigun metas and banning stock medigun could improve 6s or lead to new problems. kritzkrieg only for example. I remember people liked how quick-fix meta made the game faster a long time ago until invite teams ran full-time heavy, so it might have worked out if heavy was completely banned.