You would not have to spend time at every turn, thats just in your head.
On one hand "you"'re trying to say that there are SOOOO many reactions to manage and on the other one that popup doesnt appear SOOOO often and that its not so annoying...
There are not so many reactions to manage in DnD. The 10 seconds wasted to click "no" 10 times is just wasted 2 times * 5 seconds to plan your reaction at the begining of a combat.
I mean, even choosing the target ahead is already something that involves spending time, regardless of the TYPES of reactions available.
What's worse is that the system is bound to be completely ineffective. What if the target I select for my AoO or shield or Counterspell never actually does anything that triggers the reaction I set, but another does and I will just waste my reaction doing mothing because I didn't see it coming?