But you have a pretty direct "indirect democracy" when it comes to President. You actually say
who you want as President (to tell your state's actual Electors how they should allocate their votes in the State Electors' vote for who it should be), and this is separate from your perhaps simultaneous choice of Senator/Governor(s) which alters how two of the other compartments of government might (or might not) lean on your behalf. It's a bit of a Build-A-Bear method of trying to get your government to do as much (or as little) as you want to happen, and of course if your tendencies are in the minority then it's
you who end up stuffed.
UK version of "indirect democracy" has you voting (theoretically[1]) for the MP... who (theoretically) is allied to a given party... the party (theoretically) decides who its best choice of leader is... the leader of the (theoretically) most supported party gets to be the PM... ...which has the very real possibility of giving a PM who has an actual super
minority of public support but just happens to be the block perched at the top of a particularly wobbly jenga-tower[2] for as long as they can get away with it.[3]
Which system (of the two) is best? Not sure, but it certainly gives more practical choice (even of a low-choice field for top-dog) in the US.
[1] I've never "voted for/against” either the Prime Minister or anyone who
might have become them, only bog-standard MPs/hopeful-MPs. I wish people would stop saying they do, when no such person was even named on their ballot. Your choice generally boils down to "vote for someone you trust, to prop up someone you might think is a Complete Bastard/Bitch[1a]" or "vote for ...whoever... as long as it is the one who will help prop up the Complete B who at least is
your Complete B". But at least the one on the voting form is (theoretically) directly accountable to you, so
maybe you can directly appeal to them to try to shift things further up the stack in ways that you'd be happier with,
however crazily that needs to be accomplished.
[1a] Both terms used in an agendered way. As in "He's a bitch" and "She's a bastard" could definitely be views of various past examples.
[2] And (to continue the analogy), if removed,
could shift the balance so that the whole tower falls down, so it's the 'job' of the layers beneath to make sure they quickly rearrange themselves so that the new top block is equally offset, or slightly more, to maintain the correct balance above the badly built stack further towards the base.
[3] Looking increasingly like the election will not be soon, here. Rishi thinks he[4]'d lose (as good an endorsement for Kier as anything else, if that's your kind of thing!) and so now we're waiting for either: a) Rishi deciding that he can win, and calling it quickly before the swing towards him does what swings tend to do and swing back, b) Rishi succumbing to the
internal politics (whoever might
swing that particular sword) and their successor feeling it necessary[5] to get the supposed public support made 'official', c) Rishi (or a successor) getting 'timed out' and having to run the gauntlet by the end of next January[6], despite everything.
[4] Or, to be consistent, "his party's candidates", etc.
[5] Not good odds on that, given how many changes of PM we have had since the last election. Four mid-term changes of leader across three General Election terms (with no changes at the intervening GEs themelves). You have to go back to the 1950s for anything approaching that record (three mid-term switches across three successive GEs with continuity, although Eden
did at least call-and-win a GE in short order).
[6] Though in a "never eat the last slice of cake" way, that'll probably not be left to the absolute last minute, so more likely to be set in the lead up to Christmas (even/especially if they see a bleak campaign ahead of them, by that point in November/October/...) than immediately afterwards.