Unfortunately due to the insane design of web PKI you can't choose not to use them as every CA trusted by the root stores can sign certificates for your domain.
The static CT API does have a "names tiles" API but it's not a real/usable thing.
On top of that, to monitor you have to download full certificates and parse them all. Does that seem like a great way to do this to you?
I wasn't aware of that, I know of a few teams that do this internally and seemingly have no problems, I'll ask them next time I get a chance. Thanks for your answer.