Don't see why you need a subdomain for this, and it seems like something that may be worse on a SEO/marketing level (there's mixed evidence here, but some sources like Moz say that subdomains are treated like separate websites rather than part of the same one).
So you may not even need a subdomain for the docs site.
You certainly don't need a whole separate domain for it, especially if the only reason for it it a 'cute' domain hack without much in the way of practical value.
But then you have companies like Slack, which picked a whole new top level domain.
What's the benefit of going with the .help domain?
Go with a docs. sub domain: users will recognize the domain it belongs to and you will have one less certificate to worry about.