I'll try, but I'm sure there are people here who are better at explaining this stuff than me.
The American political system is poorly designed because it doesn't encourage power-sharing. Power-sharing tends to lead to fewer wild shifts in governing; think about how fundamentally different a Trump presidency was from the Obama presidency before it, for example, or how different a DeSantis or Trump presidency (or Pence, whatever) presidency would be from Biden's.
The electoral college is a first-past-the-post system. In other words, the first person to 270 gets the presidency. This incentivizes a two-party system in which there are two big parties, and any third parties that get momentum have their positions quickly absorbed into one or both of the major parties and are decimated. With rare exceptions - the death of the Whigs because of their incoherent position on slavery - this is what happens. For a modern example, consider how the protectionist arguments that Ross Perot was making as the Reform Party's POTUS candidate have basically been wrapped up into the white supremacist, nativist worldview of the GOP base.
In a parliamentary system, this is eased a bit because you can vote for a party that isn't one of the big two parties and still have a realistic chance at holding power. You can vote for the Socialist Workers Party's POTUS candidate in the United States, sure, but they'll never come close to holding power because of the system. On the other hand, you can vote for the UK or Canadian Greens and, assuming there's not an outright winner, they'll have a chance to form a government and power-share leadership.
Say that my riding/district in Canada votes for the Canadian Greens' nominee for representative. Great, she's our rep in parliament. And if no one wins outright power, maybe she can enter a power sharing coalition with one of the parties who wants to rule. Maybe Justin Trudeau's Liberal Party doesn't have enough representatives to form a government on their own because they don't have at least 170 Liberal reps to form their own government, so they come to the Greens and say, "hey, we'll form a government together. What do we need to give you to make that happen?" That means that my party is in the minority, but because they are needed so that the bigger party can keep power, we have leverage.
In America, there's no system for that. We don't have a parliament that picks the prime minister. There isn't enough incentive for the Socialist Workers or whomever to run for House seats, whereas if we had a parliamentary system, they'd have more incentive. They could basically influence presidential politics if the Dems or GOP needed them for a coalition.
But even Canada or the UK, though their systems are better than the U.S.'s, are not as good as they could be. They have FPTP, which means that if one party gets enough seats in parliament, they can run the government on their own. That's why the Tories in the UK have been able to run their country into the ground without interruption - they keep winning elections outright, with more than the minimum number needed to form a government without having to compromise with another party.
So it's not enough to have a parliamentary system - we'd want to get rid of FPTP. We'd probably want something like Germany's Bundestag uses, which is mixed-member proportional representation, or MMPR. The short of it is that in Germany, they vote for their own local candidate and separately for their preferred political party. In other words, let's pretend we had that here. I'd vote for my preferred House candidate - let's say they're from the Socialist Workers' Party just because we've been using that example, no other reason. Then, I'd vote for another spot in government by picking the party that I wanted to fill that spot. Basically, I get to vote for two representatives - one based on who is running in my district, and then one based on the party in general.
Let's say that in that system, I'm concerned that DeSantis will come to power, but I also don't love the Democratic party. I can safely make a vote for the third-party of my choice in my district, but then hedge that vote by also voting for the Dems just to make sure that I block the GOP with a safe vote.
When they count the votes in MMPR, all the people who won their districts get a spot in parliament, and then they look at the votes for the parties and give out extra parliament seats in proportion to the percentage of the vote each party got. So for example, if Dems win 40% of the vote, they get an extra 40% of the seats on top of whatever they won in the House districts they ran in.
This leads to WAY more coalition sharing because it's WAY harder to win an outright victory. You would have to be on one as a party to do that; there would have to be extraordinary circumstances to cause that to happen. Plus, people can vote for a third-party, and it's not a throwaway vote because depending on your district, they might really have a chance to win and wield some power.
If I were allowed to re-do the American system, I'd do this:
- Expand the House to about a thousand seats by repealing the Permanent Apportion Act of 1929. No gerrymandering - we'd have an independent commission draw these seats, but by expanding the number, there'd be fairer representation because there wouldn't be so many seats that are just ten white people who live in the same three-hundred mile wide rural district.
- Abolish the Senate. It's not necessary. It was meant to be a hedge so that white, slave-owning landholders could keep a check on whatever the House might do.
- Have the POTUS picked by the House instead of elected directly. This would allow coalition-building in the House if the Dems needed another fifty reps to form a government; they could go to whatever parties to the left of them (or immediate right) they could cut a deal with to have power, with the knowledge that they have to keep their coalition partners happy or their government would fall apart and there'd be another election
- Make it so that we have an election to retain the POTUS every five years, but that could be interrupted a) if the POTUS'es coalition puts in a Vote of No Confidence against them or if b) the party with outright control forces its leader to step down
- Run a MMPR system. I guess FPTP would be okay for House district races, but the actual apportionment in the House should be on MMPR.
Breh, that was too long and I'm sorry. I've just thought about this a lot. Hope it's not too much.