Key compromise for a single site is much less disruptive than losing control of a key that protects hundreds or thousands of sites. Generally you want to keep your scope smaller, it's safer. Rather than blanket-verify everything. Wildcards also makes it more difficult for you to see what of your names is going through CT logs.
Caddy will support wildcard certificates, but most users will not need them, because already Caddy can obtain certificates "on demand" - dynamically, during the TLS handshake. Again, the main reason for using wildcards at this point would be to reduce pressure against LE rate limits.
btw, in that scenario, even if the sites all share an IP address, you can use a TCP-level proxy that supports doing the TLS SNI exchange to determine where to send the connection on, so the proxy doesn't need any of the keys and the encryption is end-to-end.
So I guess, make sure you trust your DNS provider if you're using wildcards. Or is there another exploit I'm missing?
LE is all about DV certs -- you just need to control the web server at secure-payments.yourbusiness.com, and with DNS control you can aim secure-payments.yourbusiness.com anywhere
Any DNS-based validation is contingent on full DNS control, and that does mean FULL. CNAME records are absolute, if I CNAME foo to xyz then I'm trusting xyz 100%. I won't get an email round-trip or CAA ping for the certificate unless I'm looking for it, because CNAME implies that all things that apply to xyz apply to anything pointed at it. So the CAA record for xyz applies, not the CAA record for foo - it's not even valid to have any other record types for the same name as a CNAME record, and CAA resolution stops if it gets a valid response versus walking up to the domain root.
To be clear: CloudFlare issued a perfectly valid certificate for a perfectly valid use case, it just bothers me that I couldn't tell it was issued until after-the-fact by seeing it in CT logs, and couldn't have prevented it from being issued by the mechanisms that seem to be built for that.
Of course such access may be easier for a disgruntled internal actor so it is a risk worth considering (and mitigating via proper separation of concerns/access).