there's nothing wrong with a federal system, the problem is specifically with the US's system and how there are too many "veto points". Checks and balances and getting policy accomplished are essentially opposing goals. If you allow tons of "veto points" where having literally any control of any branch of government allows you to grind policy to a halt, then getting anything done relies hugely on gentlemanly good-faith.

In a two-party system that gentlemanly good faith eventually breaks down and you end up with our current problem, where you need supermajority control of all branches of government to actually do anything, because if you lack even one single point of control then party-line behavior will allow everything to be ground to a halt.

Parliamentary systems are better, there is just one house in most cases, and the executive is of the same party as the legislature, so when a government forms it has consensus and can execute policy. Yes, this is less checked-and-balanced, and that's a good thing, because accomplishing policy and checks and balances are opposing goals. Too much checks and balance and nothing gets done. If everything is fine that's great, but our system has been deadlocked for 20 years now, things are not great, and nothing can be done about it.

And there are still an executive and judicial branches in a parliamentary system, it is still a federal system, just not the American federal system.

The real "checks and balances" is ultimately voting. Having snap elections allows that check to be manifested much more readily when the government begins to go off the rails of public opinion.

(the queen is actually a very interesting apparatus in the british government... apart from having some kind of maximum duration between elections, you are dependent on someone to decide when to call a snap election. Obviously you can't really rely on a government that is completely off the rails to call an election on itself, and party line voting poses obvious problems. So how do you deal with it? An oracle machine (in the crypto sense) that exists outside the system and can operate independently to decide when to call an election. Which is what the queen does, she can dissolve parliament and call an election.)