You're implying that they should???
You're implying that they should???
Note that this is on the order of trillions of useless computations at least per year since almost everyone just uses a CSPRNG or HWRNG available in all modern computers to generate their keys sanely.
Now, for CAs, sure because that is a very small number of certificates. But that's a completely different discussion and also however eMudhra managed to lop off all of the entropy except for the final byte was wildly incompetent and not something a layman would even consider doing.
It's also not the job of the CA to detect you being an idiot. You can go post your private key online after getting your certificate if you so wish, the CA may revoke it if they find out but they're just in the business of helping you secure your communications with others. If you wish for them to actually be insecure... You are silly, but that was always allowed.
In fact I assumed that’s why somebody might explicitly choose “4” as their key: to make it as easily detected as “TK” in a copy edit, or a prefix-designated API key in a repo, or an “@example.com” that slides by into a serious environment.
We really go on a pinky swear across the public CA ecosystem?
By pigeonhole principle, nearly all numbers have to have a Kolmogrov complexity within some constant of their own length, meaning they are algorithmically random and will by definition pass every statistical test of randomness, so you lose surprisingly few bits entropy per assertion this way.
And again, you have to actively work to get a "private key" of 0000 ... 0-255. If you want to be stupid it's not really the CA's job to tell you not to be. It's their job to verify your identity. And, again, a CA itself is a totally separate beast where this thinking does not apply. If you want to be secure it's easy to be secure and if you don't want to be... Why should anyone else care? You are only hurting yourself.