A signature on a certificate doesn't allow CA to snoop. They need access to the private key for that, which ACME (and other certificate signing protocols in general) doesn't share with the CA.
Modern TLS doesn't even rely on the privacy of the private key 'as much' as it used: nowadays with (perfect) forward secrecy it's mainly used to establish trust, and after which the two parties generate transient session keys.
* https://en.wikipedia.org/wiki/Forward_secrecy
So even if the private key is compromised sometime in the future, past conversation cannot be decrypted.
Adding multiple signatures to a certificate would be difficult because the extensions must be a part of the certificate which will be signed. (However, there are ways to do such thing as web of trust, and I had thought of ways to do this with X.509, although it does not normally do that. Another way would be an extension which is filled with null bytes when calculating the extra signatures and then being filled in with the extra signatures when calculating the normal signature.)
(Other X.509 extensions would also be helpful for various reasons, although the CAs might not allow that, due to various requirements (some of which are unnecessary).)
Another thing that helps is using X.509 client certificates for authentication in addition to server certificates. If you do this, then any MITM will not be able to authenticate (unless at least one side allows them to do so). X.509 client authentication has many other advantages as well.
In addition, it might be helpful to allow you to use those certificates to issue additional certificates (e.g. to subdomains); but, whoever verifies the certificate (usually the client, but it can also be the server in case of a client certificate) would then need to check the entire certificate chain to check the permissions allowed by the certificate.
There is also the possibility that certificate authorities will refuse to issue certificates to you for whatever reasons.
It might be interesting for ACME to be updated to support signing the same key with multiple CA's. Three sounds like a good number. You ought to be able to trust CA's enough to believe that there won't be 3 of them conspiring against you, but you never really know.
Edit: I'm gonna be rate limited, but let me just say now that Certificate Transparency sounds interesting. I need to look into that more, but it amounts to a 3rd party certificate verification service. Now, we have to figure out how to connect to that service securely lol... Thanks, you've given me something to go read about.
And a malicious actor can abuse this fact.
CT logging is mandatory, and even a single missing cert is probably going to be an existential threat to any CA.
The fact that someone is checking is already enough of a deterrent to prevent large-scale attacks. And if you're worried about spearphishing-via-MitM, you should probably stick to Tor.
An active adversary engaging in a man-in-the-middle attack on HTTPS can do it with the private key, as you suggest, but they can also do it with a completely separate private key that is signed by any CA the browser trusts. There are firewall vendors that openly do this to every single HTTPS connection through the firewall.
HPKP was a defense against this (https://en.wikipedia.org/wiki/HTTP_Public_Key_Pinning) but HPKP caused other, worse problems, and was deprecated in 02017 and later removed. CT logging is another, possibly weaker defense. (It only works for CAs that participate in CT, and it only detects attacks after the fact; it doesn't make them impossible.)
It is called a private key for a reason. Don't tell anybody. It's not a secret that you're supposed to share with somebody, it's private, tell nobody. Which in this case means - don't let your "reseller" choose the key, that's now their key, your key should be private which means you don't tell anybody what it is.
If you're thinking "But wait, if I don't tell anybody, how can that work?" then congratulations - this is tricky mathematics they didn't cover in school, it is called "Public key cryptography" and it was only invented in the 20th century. You don't need to understand how it works, but if you want to know, the easiest kind still used today is called the RSA Digital Signature so you can watch videos or read a tutorial about that.
If you're just wondering about Let's Encrypt, well, Let's Encrypt don't know or want to know anybody else's private keys either, the ACME software you use will, in entirely automated cases, pick random keys, not tell anybody, but store them for use by the server software and obtain suitable certificate for those keys, despite not telling anybody what the key is.