As much as I'd like to push the idea of the external drive for the user folder, it feels like a workaround/hack, it diminishes the elegance and simplicity, it adds some security considerations. It's just not ideal.
If you have to be worried about security in this context: People who might snatch an external drive, might as well snatch the whole mini.
I also ran into an issue with this VPN software "ExpressVPN" for some reason it won't work off my user from an external USB, but it will work if I use the user on my internal SSD. I tried creating new users both on external and internal drives, same results. So this is one example of an external user folder having unexpected results vs internal.
Did you try an external Thunderbolt drive? The different way of implementation vs. USB bears a good chance it would work on a TB drive.
Apart from that I don't know whether the special kind of software and related security considerations lead to the problems you describe - or whether the software is simply poorly implemented.
Besides - even with 128GB, there is still room for a couple of programs after an OSX installation, if required. It's just the bigger save data that has to go elsewhere.
What if Apple had included an additional internal NVMe or SATA slot? Previous Mac Minis did have space for 2 drives. That would have been great, but not as profitable for Apple as soldering storage and then charging an arm and a leg to upgrade it. This is the root of the complaint, the external path is not elegant and the internal path is for rich people, not for the rest of us™.
Take a look at the teardown of the 2018 mini and tell me where you would find the room to have an internal NVMe slot (leave a lone a 2.5" bay)!
Apple has decided to go for a powerful desktop-class CPU in the 2018 mini and that requires a powerful cooling solution, which takes much more space than the one for the mobile-class CPU's in former generations. They also decided to offer upgradeable Ram slots (which had been demanded by many users), which take quite some place as well.
So for me the lack of an internal drive slot is not the bad, bad Apple trying to best its customers, but instead a technical necessity resulting from the decision to position the new mini in the semi-professional sector, with higher-performing hardware requiring more space in the mini's casing.
You could argue that Apple should have designed a new housing then, instead of re-using the old molding tools, but that would have taken more time & resources, thus increasing the already high price of the 2018 mini even more.
Apple is currently on a way to increase product prices all across the board to satisfy investors. This sometimes involves a re-positioning of a product like the mini, changing the target group and making it more costly for the interested private user.
A top manager of Porsche was once asked in an interview about a more affordable entry model. His answer was around the lines of "a used Porsche is our affordable entry model". I feel that Apple is heading a similar way.
