Even larger companies can work well with that model, traffic also tends to be cheap enough that you can spread across different vendors to avoid lock-in. And in that case, your sysadmins can sit wherever they want, no need to be physically close to the servers.
Also, as there's much less knowledge to be a dedicated server provider, competition is strong and prices are comparably low.
I used to spin up dedicated servers and then put an overlay network + a simple set of tools to spin up containers on them years before Kubernetes etc. was a thing, and we'd have a "global" (we had VMs in Asia, dedicated servers in Germany and colocated own servers in the UK) unified deployment mechanism that let me spin up containers wherever with a one-liner. Having a few extra dedicated servers with spare capacity standing by still made the whole system far cheaper than e.g. AWS, even if you attributed my entire salary towards it (I spent nowhere near all my time keeping that running).
It's easy enough to find consultants that can set up systems like this that abstracts away the dedicated hosting providers so you can mix and match and move with ease - especially today with options like Kubernetes.
If I was to go back to doing consulting I'd probably look at finding a way of packaging this kind of offering up behind lots of marketing speak and offer some sort of "abstract" hybrid private cloud layer on top of a choice of dedicated hosting providers to make that kind of hosting palatable to execs who refuse to believe the cost saving potential because they've never dived into the actual numbers (oh, the amount of time I've spent building out spreadsheets with precise cost models that'd get promptly ignored because someones had heard from a friend that company X swore vendor Y was cheap and believed it blindly)
Also it is a major pain point getting anything done with IT operations.
Like the Oracle database server that half the department relies on stops responding on a Friday morning and it takes all day to determine the hard disk is full and fix it. I had never before worked at a company where this happened multiple times.
Or operations saying they were unable to restore a windows server hosting a database server and now everyone has to scramble to update their connection strings because operations somehow cannot use the same domain name for the new machine.
If you're Netflix, cloud is probably not that much more expensive than owning your own servers. Maybe even cheaper. But you're not getting Netflix prices.
But even if you're small fry you should however start regularly talking to your provider and go through a regular cost-cutting exercise and talk to them about how you're looking at provider Z and have been asked to cost out managed servers and on prem options.... You won't need to get very big before that starts paying off.
If your competition is doing this and you're not, and hosting costs starts becoming a big part of your cost base, you won't be able to compete.
Long term I think we're going to see disruption here to the point of startups failing because of competitors copying their idea but being better at driving down hosting costs by not being afraid of going to dedicated hosting or hybrid solutions (hybrids are my favourite - if your stack can be deployed semi-transparently both on dedicated servers and cloud you can go much closer to the wire on your dedicated servers by being prepared to spin up cloud instances to take care of spikes; ironically having the ability to spin up cloud instances makes relying on cloud services even less cost-effective)
I'd also expect to see more "hybrid" cloud offerings with companies offering you operations-as-a-service by giving you a virtual cloud type interface where they don't actually own a cloud service themselves but helps you abstract away cheaper hosting providers. You can already find plenty of people who'll e.g. run Kubernetes setups for you, so taking the step to do more cost-optimization on the backend is natural (and I'm sure there are people who'd do this for you today - if I was still doing contracting I certainly would be offering that - and maybe someone is already wrapping it up as a service offering; I haven't kept up on that market)
