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.