The big three root store programs are run by Apple, Microsoft, and Mozilla/NSS. Most (all?) Linux distros are based on the Mozilla store. Until recently, Google also used Mozilla’s store for things like ChromeOS and Android. They just recently announced that they’re gonna start running their own program though.
FWIW the browsers seem to do a pretty good job of policing CAs. Probably better than most end-users would do.
I’m on iOS and don’t have an Android or ChromeOS device handy. I don’t see a way to remove a cert from Apple’s iOS trust store (settings just tells me what store version I’m running). There may be a way to do it using mobile device management (MDM) tools.
Obviously this is all addressable in theory, but now you’d need some kinda policy system baked in pretty much everywhere.
Your website hands me a cert. I have never seen it before so I make sure CA says it's legit. From then on I keep using that same cert to connect to you, and CA no longer matters.
The CAA record is useful only at the time a certificate is issued (signed) by a CA.
A client has no way to know what the CAA record was at the time the certificate was issued -- a browser cannot ("at acceptance-time") use the current value of the CAA record to determine whether a certificate was properly issued or not.