Deadlock is not the worst thing, and the solution to it is not necessarily to remove as many locks as possible.
The actual problem in the US right now is that checks and balances are strong enough to allow one party to block things, but not strong enough to deter waiting until your party stochastically has enough power to get things done. This is exacerbated by having one party's ideologically committed to having the government do less.
In previous decades, stuff like earmarks greased the wheels enough to get things done (but an effective PR campaign against them got them banned). You could also fix deadlocks by strengthening the checks to force compromise among factions, like by coupling automatically expiring legislation with requirements for big super-majorities.
Since Congress makes its own rules, and 51/49 is enough to change a rule ('the nuclear option'), supermajority would have to be a constitutional amendment... And then 45% would be enough to halt government. I guarantee you this would then happen regularly.
Other systems have mechanisms to force elections if deadlocks are persistent. Of course, you also need mandatory voting, PTO for voting, full franchise, etc and that isn't going to happen in America while this Supreme Court lasts.
That was the problem with the Senate's supermajoriy requirements: basically the only thing holding them in place was convention, so they fall in the face of someone willing and able to make unsentimental tactical power plays.
IMHO, someone like McConnell would have behaved very differently if he knew his opponents could block him just as easily as he has blocked them. His apparent effectiveness is almost entirely a result of his greater willingness to hypocritically use then discard convention when it gets in his way. He'd never have gotten his tax cuts or judges if he wasn't able to bend the rules.
> Other systems have mechanisms to force elections if deadlocks are persistent.
I think something like that could be a genuine improvement.