Does cloud save on time?
Sometimes it does outright, see Heroku, or AWS Lambda.
Sometimes you try to bite more than you feel comfortable to chew, and get bogged down configuring kubernetes or terraform when you don't need as much.
In the simplest case, I think, the cloud is also an inevitability. Can you imagine starting up by buying some used servers, colocating them in some datacenter, calling an operator when they need tweaking a BIOS setting, scheduling a visit and downtime when you need to replace a failing NIC, or a degrading HDD? This is what life without the cloud used to look like. Yes, a EC2 instance is cloud.
Of course you can try a middle ground, dedicated hardware managed by a provider, e.g. what Hetzner offers. If your load is very stable and predictable, your stack is very simple and mature (an RDBMS + Apache + PHP, ore maybe Erlang / Elixir), and you are ready to either keep a hot spare or sustain rare but prolonged downtimes, you'd be fine with a small amount of dedicated hardware.
A large amount of dedicated hardware may be economical, but only at quite large scale (see, well, Facebook).
Also failed PSUs or hard drives don't require downtime, since those are hot-swappable and redundant in servers. If you want to optimize for (physical) hands-off operation you can even add an extra 1-2 hard drives that are configured as hot spare that the RAID (be it hardware, software or ZFS) will automatically use in case one of the active ones fails.
And the performance difference between dedicated hardware (be it dedicated server or your own) can be quite staggering compared to what you actually get from the cloud providers.