I played Skyrim after completing BoTW, and I found Skyrim to be thoroughly enjoyable, aside from some clunky movement and melee mechanics. Despite its age, I think Skyrim holds up really well and is a great experience, even after 200 hours. The repetition in the quest giving has me declining quests in the end game....but I still find running through an undead infested cave or temple with dawnbreaker extremely satisfying. =p
I don't totally agree with your assessment of the BoTW shrines all feeling unique or memorable. I got to a point where I had more than enough hearts to defeat Ganon and did not feel the need to continue finding shrines, as many had similar mechanics or mini bosses to fight yet again. That said, I really have no major complaint about them either
