Interesting. We haven't had any issues with confusion about readied actions or other stuff. Can you offer an example? What is going on that people would miss their turn?
I wouldn't get rid of these things unless you find no alternative, as it would require a lot of tweaking.
Many features use your reaction, besides Counterspell and Shield, others such as Uncanny Dodge, Skirmisher, and Arcane Deflection (five reactions my current character has!).
Removing OA would hurt classes and feats which incorporate OA as a key feature.
Removing Ready would prevent and complicate situations where one creature is prepared to act depending on another's.
What is making Countering hard? You spend a 3rd or higher level slot to prevent an enemy caster from completing their spell. Is it the time for the extra die roll and figuring out what DC is needed? In that case maybe Countering could instead impost a penalty against the incoming spell, perhaps making it miss, or offering a bonus to the saving throw for the target(s)?