Why would we have a PM? We already have the Speaker of the House and the Senate Majority Leader. And the PM wouldn’t be able to exercise any executive powers unless you burned the constitution, because separation of powers.
There’s not really a good reason to adopt a parliamentary system like the UK’s for example if we were to completely reform the government imo. Or to have a PM separate from the president at all.
I was gonna disagree, but I couldn’t actually think of a functioning stateless ideology which allows private property. Anarchism is inherently for abolishing private property, so that’s out already. That mostly just leaves you with "anarcho-"capitalism which is just replacing the government with an ultra-capitalist power structure and decimating social mobility, it’s just an undemocratic state but shittier…