Not using a cloud provider is asinine. You can use layered encryption so the expected lifetime of the cryptography is beyond the value of the data...and the US government themselves store data on all 3 of them, to my knowledge.
I say US because the only other major cloud providers I know of are in China, and they do have a vested interest in South Korean data, presumably for NK.
Can you articulate what particular advantages the US would be pursuing by stealing SK secret data (assuming it was not protected sufficiently on AWS/GCP to prevent this, and assuming that platform security features have to be defeated to extract this data—this is a lot of risk from the US's side, to go after this data, if they are found out in this hypothetical, I might add, so "they would steal whatever just to have it" is doubtful to me).
The US also has a secret spy facility in Pine Gap that is believed to (among other things) spy on Australian communications, again despite both countries being very close allies. No Australians know what happens at Pine Gap, so maybe they just sit around knitting all day, but it seems somewhat unlikely.
[1]: https://www.theguardian.com/us-news/2015/jul/08/nsa-tapped-g...
Why do you think USA wouldn't lie, cheat and spy on someone if it had a benefit in it?