Re. the number of machines, it's something I've encountered as an obstacle from a fair proportion of people I've spoken about password managers to. I think its more a perceived issue than a real one.
Just spitballing which systems I would realistically want access to passwords on, at a minimum, includes: personal desktop, personal laptop, tablet(s), cellphone(s), family (parent, sibling, in-laws, etc) computers, office desktop, office laptop.
In my case (many cases?), the latter two prevent software installation, so I would need to manually type from a manager synced on my cell. Which really is no different to what is required for 2FA - just a longer character string. Overall, a some setup and synch related inconveniences but not to a damaging degree, which is why I think this is more a matter of perception - once you think through where you're typing passwords it appears less of an obstacle.