Updating and replacing system Python takes tremendous blood and treasure. Compiling python from scratch, updating symlinks, resolving dependency issues and finally debugging the whole thing is no small endeavour. Been there, done that; never again.
I've done this dozens of times, didn't seem like that big of a deal? I think the place this might have fallen over is the "updating symlinks" part. Don't replace the system Python, install yours alongside it. They don't need to know anything about each other; aliases in developers profiles and full paths in services/scripts.
Yup, stick it in /usr/local and place that in your PATH and Python search path before other dependencies. If you want to be fancy, put it somewhere in your home directory so other users on your same machine cannot be affected.
It's really not hard. I do this with other compilers and don't really have issues, though I tend to package it up into a container if I'm going to ship it (e.g. build environment for a team, interpretor for a production service, etc).
Or you could, just like on other platforms and with other languages, use virtual environments with a version manager such as pyenv for your development environment. Combine that with pipenv and you get pretty painless python development. To be fair, some of this stuff is more recent though.
Here is an excellent short blog describing all this and how pyenv and pipenv click together to create a virtual Python environment, that is completely independent of your OS vendor's runtime: https://gioele.io/pyenv-pipenv
This stuff is definitely quite new, and I guess the need for it has risen as a consequence of all the great new features that have shipped in Python during the last few years.
I recently had to write an utility script in Python. I chose to use Python 3 and type hints syntax, requiring at least Python 3.6. This was a problem when I realized some of my team use Ubuntu and Debian versions that ship with Python 3.5 (not to speak of Macs with Python 2.x, but these guys use homebrew anyway). Plenty of time was spent researching virtual environments and writing deployment instructions, and I ended up using pip in pyenv (but stopped short of using pipenv, since creating private distributable packages with it seemed convoluted.)
It's hard if you're trying to update the system Python and need to upgrade every dependency for that but if you just want to have, say, “python3.7” in your path it's just a couple of commands:
(This was on a Ubuntu LTS system)