It says a lot about Stripe's workplace culture that they're not afraid of this.
I hope you're joking, because that seems like a very silly reason in the age of LinkedIn and recruiter databases. It's probably very easy to find a relatively up-to-date list of employees for any given company out there.
My guess is that most small companies don't do this simply because they don't even consider that it would be a nice gesture to publicly recognize more than just the top execs.
You are right that with things like LinkedIn you could probably get a lot of this information, but it's enough of a hurdle that execs still think it's worth it.
But in a growing company above a certain size keeping such a page up to date can be a pain.