(DigiNotar was trustworthy right up until people discovered that it had been compromised. StartComm actively hid that it had been bought by WoSign; it took people some digging to turn this up and verify it. Other CAs have routinely denied that they had problems when they did.)
Even if you could, picking an especially trustworthy CA doesn't add any extra security for your website, because you are actually dependent on the security of all of the CAs out there, any of which can in theory mis-issue a TLS certificate for your site. Sure, there's CAA records, but this only helps if the CA actually follows the rules properly; CAs can fail here at both a technical and a business level. (One CA recently proposed that it should be allowed to ignore CAA records if the domain owner told it to.)
Even attempting to do basic checking of a CA probably doesn't make sense at a business level unless you're buying certificates in bulk. Suppose that you're buying four TLS certificates and the best price you can get is $30 per certificate per year, or $120 in total for a year. How much engineer time does it make sense to spend in order to pick the most 'trustworthy' CA (ie one that is likely to remain trusted by browsers for a year), given that CA de-trusting is an extremely rare event and if it happens, you're only out another $120 to buy certificates from the next CA?
(I'm the author of the linked-to entry and as you can tell, I have opinions on CAs and the TLS ecosystem. One of them is that Certificate Transparency is a really big deal because it removes a lot of the 'trust me' from the whole CA ecosystem.)