I am totally sympathetic of that because I also interact with users who aren't tech savy and don't want to clear out everything. But, you can clear your cookies and cache without losing their browsing history since those are different options to check when deleting.
However, if you want to avoid your end users from having to do this themselves, you can always use IT management software that will clear the cache and cookies out of all their browsers on their behalf. So post-upgrade, send out a command that will clear out cookies/cache.
Finally, I would imagine that this issue, at max, happens only twice per year (since Esri only releases new versions twice per year). I realize that non-tech savy people don't understand why any of this is necessary, but I don't think it's a lot to ask of people to clear their browser cache up to twice per year. (I know you're just stuck in the middle, like myself, and have to deal with people complaining. But the only alternative is it just never upgrade ArcGIS Enterprise).
Honestly, I would leave this decision to the organization. What does the organization value more? Not clearing out cookies/cache a couple times per year? Or never upgrading Enterprise because people don't want to clear their cookies/cache?
