TLS 1.3 is definitely better than previous versions. Note however that it wasn't published until 2018; Tarsnap's transport layer has been in use since 2007, before even TLS 1.2 was published. If I had used TLS at the time, it would have been TLS 1.1. Hopefully you agree that would have been a bad thing?
I mean, TLS 1.1 isn't a good thing, but which <TLS1.3 bugs actually would have impacted Tarsnap? SMACK, maybe? Probably not POODLE, given the ciphersuites you'd have locked down to. Not BERserk (you'd never use NSS). The TLS BB'98 attacks didn't hit any library you'd actually use. No Triple Handshake, since you wouldn't do renegotiation. No BREACH, TIME or CRIME (they don't fit Tarsnap anyways). No RC4 (lol). No Lucky13, for the same reason as no POODLE. No BEAST, because you don't do Javascript. And now we're back to 2007 (or pre-2007) for attacks on TLS.
It's possible that I could have taken TLS 1.1 and removed all the broken parts, sure. I mean, that's pretty much what TLS 1.3 is.
But frankly I trust my ability -- both now and in 2007 -- to use standard cryptographic algorithms to build a new protocol far more than I trust my ability to remove all the crap from TLS 1.1.
Heartbleed isn't a TLS vulnerability any more than an overflow in GnuTLS is.
The threshold question is, "could this vulnerability be reasonably expected to recur in independent implementations of the protocol?"
As for stripping back TLS 1.1 --- it wouldn't take much more than simply picking a single ciphersuite and requiring TLS 1.1. You wouldn't need to know, for instance, about export ciphers.
Why does TLS make you twitch? Does that apply to TLS 1.3?
[1]: https://loup-vaillant.fr/articles/rolling-your-own-crypto