We (my team) hit this as well with an automated compatibility test running on Ubuntu 16.04. I decided to just change the test to install Python 3.8 from the deadsnakes PPA, and then use get-pip.py to install pip.

https://launchpad.net/~deadsnakes/+archive/ubuntu/ppa

This does change the test to no longer use Python 3.5, but considering a) we'd already dropped support for Python 3.5 for the code we were testing, b) Python 3.5 is EOL and c) Ubuntu 16.04 will be soon, it didn't seem worth trying to stay on 3.5.