I've worked with teams on both sides, and everyone is gonna have to deal with figuring out how to run at scale, it's just different ways of achieving that.
I've worked with teams that manage their own infrastructure with dedicated servers, and not having to think about scaling for a long time as the one beefy server could just take whatever load you threw at it.
I've also worked with teams who don't manage their own infrastructure and thought they were ready to scale without issues, but once the scale actually happened, it turned out there was more things to consider than just the amount of servers you run, race-conditions were everywhere but no one thought about that.
Definitely a case of "right tool for the right job", but I don't think it's as easy as "Self-managed: harder to scale, PaaS/Cloud: easy peazy to scale".