A good manager isn’t looking for polished answers in a phone screen. Rather it exists to validate that it is worth my and your time to meet in person.
Eg. I’ll provide more context on my needs as the hiring manager (often the recruiter explains the role poorly). Then I’ll ask a few questions related to the role that are pretty basic to validate your background isn’t BS.
So if you get screened out here despite nailing the questions then the manager is hiring on the wrong criteria (likability?) and you probably don’t want to work for them anyway.
I suspect many of the gut feelings people get doing phone interviews are a matter of luck.
I do appreciate the convenience of a phone interview, but it would be incredibly good for my peace of mind if more of them could start off with a simple email conversation to introduce each other. I tried to do that myself for a brief moment where I was interviewing people, and I thought it went quite well. (My boss, wondering how he almost didn't hire me, put me in charge of hiring someone like me, which was surprisingly non-destructive, but I'm grateful I don't need to do it on a regular basis).
With that said, I really dislike the jobs where they ask you a bunch of random questions right in their application form. That's way too much work when your answers to those questions probably won't even reach your interviewer anyway.