You might want to think about existing surveillance systems. Analysis of telephone traffic is often done purely on the CDR (the caller, callee, and length of call, in simple terms) without the equivalent of deep packet inspection to read the HTTP request, which would be analysis of the actual audio data themselves. The HTTPS case would likewise need just the total octets transferred over the TCP connection for fingerprinting.
There's a lot of glib handwaving in this discussion about identical sizes, not based upon actual measurements of the Debian archive. I quickly looked at the package cache in one of my Debian machines:
jdebp% ls -l|awk 'x[$5]++'
-rw-r--r-- 1 root root 3314 Feb 16 2018 nosh-run-freedesktop-system-bus_1.37_amd64.deb
-rw-r--r-- 1 root root 35190 Dec 14 2016 redo_1.3_amd64.deb
-rw-r--r-- 1 root root 1114546 Feb 25 2018 udev_232-25+deb9u2_amd64.deb
jdebp %
It turns out that in practice size alone almost does uniquely identify package in this sample. The other file that is 35190 bytes is version 1.2 of the same package, leaving just 2 possible ambiguities out of 847 packages. It seems likely that this holds after encryption as well.So the remaining question is how much HTTP pipelining ameliorates this, which no-one here has yet actually analysed.