It's fantastic if you want to build TLS testing tools, or if you want a codebase to reason about TLS with.
What, however, hinders adoption as a "working man's" TLS library? Neglecting performance and variety of cipher support, would or should anything prevent me from using Tiny TLS to secure channels between "inner circle machines" (that talk to a set of well-known participants)?
If you're trying to deploy pure-Python applications, I like tlslite. Of course, I have to say that, because Trevor is much smarter than me.
Personally, I think your realistic production choices are OpenSSL or NSS.