You outsource some of the sysadmin work, but not all of it. Cloud servers have plenty of their own failure cases, some of them unique. Physical hardware is actually quite reliable and if you follow the same practices you should in the cloud - namely automatic failover, eliminate single points of failure, etc then the differences decrease.
Dynamically scaling load is only really interesting if the load is extremely variable. You could just buy 5x the dedicated hardware, which will likely be able to serve 10x the traffic and may still end up paying less. Who cares if it sits idle most of the time.
Now Spotify, like Netflix probably has extreme variance in load, much more so than a normal company. So maybe the cloud works for them. But that's not a common situation at all.
It's definitely common for IT staffing costs to increase rather than decrease with a cloud transition, at least so far. Part of the problem is that you often are trading off sysadmins (relatively cheap) for engineers (relatively expensive), as you reengineer your system to run on top of ephemeral, distributed cloud servers, with new failure cases and new technology stacks. This is often justified on the basis that a large chunk is one-time engineering cost that will pay for itself in the long run. But that's a speculative bet, especially considering how much technology churn is happening so far (e.g. a bunch of companies that invested heavily in early 2010s cloud stacks are now re-investing in Docker). It's possible things will stabilize enough for such companies to eventually lay off many of their distributed-systems engineers and devops staff, and go more into cloud-autopilot mode with low IT headcount and lower staffing cost than pre-cloud-transition. But I don't think many companies are there yet, and I wouldn't bet a lot of money on it myself.
Google and their famous customer support, yes. Worried they might be, but more than you? For them, the cloud is one of many revenue streams, and nowhere near their most profitable. For you-cloud-customer, a website outage might mean you don't have a revenue stream anymore. It could make the difference between making payroll and shutting down next week. I bet you'll be much more worried than Google will ever be.
Googlers might be more skilled than your ops team, yeah, but I would never bet on huge companies to worry about the fate of something that is not their main revenue generator.
Dynamically scaling load is only really interesting if the load is extremely variable. You could just buy 5x the dedicated hardware, which will likely be able to serve 10x the traffic and may still end up paying less. Who cares if it sits idle most of the time.
Now Spotify, like Netflix probably has extreme variance in load, much more so than a normal company. So maybe the cloud works for them. But that's not a common situation at all.