As someone working at a dev shop/full-service-agency mostly using cloud(Azure) and having also managed server on my own in the past it's an easy breakdown.
1: We have a dozen or so regular clients and being in a relatively high salary cost country, while our cloud bill isn't insignificant it's still far less than one full time employee, even less so than having 24/7 on-call handled (we have large enough 24/7 critical clients).
2: The cloud provides broken down billing, it's easy to pass it to the customer and just point to it, having our own employee we would need to structure up the billing process somehow. Our customers are outside of the IT field and doesn't care as long as it works and doesn't cost too much (it's a mostly fixed expenditure and easily separable from our development hours).
3: We have one client that does on-prem (partly out of habit) that's actually looking at parts to the cloud, partly because they've expanded internationally but I wouldn't be surprised if it's a bit of testing the waters since they have to spend a fair bit of their time on security and stability (security doesn't go away entirely of course but I'd be more sure of my backup processes on a large cloud compared to just locally).
4: I'm a tad on the fence of cloud-api's:
On the positive side: No need to implement a bunch of systems(badly?) and no need to build/install monitoring tools for those (and the extra administration burden that comes with updating those tools for X number of clients).
On the negative: There's a tad of churn on some cloud-api's, luckily Azure is mostly stable with plenty of migration time until you come around to a customer again (reading about Goog's churn feels like horror stories), and yes there is a bit of vendor lock-in if you go all-out (luckily we've not seen any reasons to change over).