> HTTP/1.1 alone is a trivial protocol

Eh? CWE-444 would beg to differ: https://cwe.mitre.org/data/definitions/444.html

https://http1mustdie.com/

> the alternative is trusting the client's much more complicated TLS stack and its HTTP stack.

An attacker doesn't get to attack client's HTTP stack without first piercing protection offered by TLS.