Presumably if LetsEncrypt goes down and stays down for a week, the sites that go down are the ones that see that their CA went down and at no point in the week take the option to get certs from a different CA?

I guarantee that there are a ton of sites out there not monitoring their certs.

Including Microsoft, Starlink, Github, Cisco:

* https://www.keyfactor.com/blog/2023s-biggest-certificate-out...

"A ton" being a misspelling of "the vast, vast majority".

Are there alternative CAs that are anywhere as easy to deal with as Lets encrypt?

acme.sh supports multiple CAs there is even a RFC for CAs that describe the api.