An initiative roll would be just as easy. And it solves the issue through the simple fact that bias rolls are a thing. The current issue is that initiative on AI is just so high that putting points into iniative doesn't feel rewarding unless you really put some effort into it.
This effect than extends over time as enemy iniative grows over the course of the game with level and gear.
Whether someone puts 10 points into initiative or 5, there should be a noticeable change in game play. Things don't currently work that way.
Law of averages dictates that initiative roll would present that change presentably. It would change how often one goes last or first or land in-between.
Also, there's no such thing as truly random. It'd be pseudo random at best technically. We were discussing how bias the rolls should be and to whom.
That's one algorithm function call to assign initiative roll value with one call from combat start passing in the initiative stat fir each character on the screen. Can't get much more simple than that
Not that your way couldn't work but i;m not a fan of it.
EDIT:
Hell, adding the algorithm would change game experience without needing to touch initiative values anywhere else
None of what you said is decidedly wrong, it just doesn't address the issue, and if we're being serious the issue has nothing to do with the enemy initiative being too high, but instead has more to do with the stat system for PCs being utterly broken leading to players having to scrounge initiative wherever they can get it. A roll only has any effect on the user experience in the short term, over a long period the system would still prove to be broken with a few small instances of it actually paying off. As I said, they are unrelated issues.