And plenty of datacenters will be happy to give you some space in one of their racks.

Not wanting to deal with backups or HA are decent reasons to put a database in the cloud (as long as you are aware how much you are overpaying). Not having a good place to put the server is not a good reason

If anyone's curious about the ballpark cost, a carrier-owned (?) DC near me that publishes prices (most don't) advertises a full rack for 650€ per month, including internet @ 20TB/month @ 1 Gbps, and 1kW power.

Though both of which are probably less than you'd need if you needed a full of rack of space, which I assume is part of the reason that pricing is almost always "contact us". I did not bother getting a quote just for the purpose of this comment. But another thing that people need to be less afraid of, when they're looking to actually spend a few digits of money and not just comment about it, is asking for quotes.