"All [webhooks] are is a promise by an application or API: “when this thing happens, I’ll send this HTTP request with this data.”"
It's nice to see that all the hype really just boils down to generalized pingbacks[1]. Now, having a standard is great -- I'm not entirely sure we have a standard yet, though. It's more like a fancy name for pingbacks that aren't just for blog posts.
I'm also not entirely sure if I'd prefer webhooks for eg. processing emails. Emails are naturally "push" -- they get pushed via SMTP. I know that people are scared of email/SMTP -- but it seems quite a lot easier to make sure you don't loose any "events" with SMTP than with HTTP(S).
What if your site is down for a few minutes, just as some service out there tries to "ping" you with a webhook? Email handles that.
I think what most people seem to mix up is that handling "real" email may be hard -- but looking for a well formed subject that exactly matches some regex, then parsing that, isn't that hard. Everything else you can either bounce (a little dangerous) or just drop (not quite as dangerous).
Mailing-lists work. What you need isn't much more complicated. Maybe allow for a mime-part with a json or xml, or some other well-formed body. Use gpg or smime to encrypt data, if you need something more than a short hash/token.