Servers, for the most part, just work. In DC climate-controlled environments, hardware failures is exceedingly rare. Apart from harddrives, most hardware will happily tick along for a decade, if not longer.
Sane production-grade OSes (read: not Ubuntu) will also happily run for literal years with zero human intervention. For obvious reasons, it's a bad idea to not patch your systems, but things will continue to "just work" pretty much forever unless you're running really shitty code.
For renting vs buying servers, there's upsides and downsides. Buying gear is far far cheaper if you plan to be around for more than a year, but renting dedicated servers gives you a lot more flexibility -- to provision a new server, you hit a button in their online panel, wait 15 minutes, then let your deployment strategy take care of the rest.
I find it almost mind-boggling that AWS and friends have convinced people that it's normal to spend ridiculous amounts of money for fairly "meh" service specs in what's essentially VMs.
Not to mention that at that scale you have plenty of redundancy and, if your ops team knows what they're doing, automagic failover / HA. Anything that happens can easily "wait till Monday", no need for 24/7 anything.
And my experience from providing devops services to clients on a contract basis is that the clients who use cloud services tends to need more, not less, devops assistance.
As an example of the latter bit, if you are running your own hardware and need to add another host and you do not have a spare lying around, then you need to order one. It has to be shipped. Someone has to unpack it. Someone has to make sure that the data centre has sufficient power. Someone has to install it, its power and its network cables. Each of these steps takes time, but also each step is an opportunity for friction.
By contrast, with a service, you would just add a new host. Five minutes later you are up and running. That gives you an operational nimbleness that you wouldn't otherwise have had.