What I mean by 'interrupts' are player actions that interrupt the actions of other players or, interactions between other players and the DM. For example, some characters have specific types of reaction actions they can interject in a way that is out of order (like the warding flare class ability of Light Domain clerics).

I have noticed that a number of 5e replacements have tried to incorporate changes that try to significantly reduce the amount of time / effort it takes to resolve actions. However I have been thinking about how interrupts themselves could be streamlined.

I think what makes them bad (reaction mechanics that is) is that they halt the flow of game, now for one or two abilities that key off a reaction is one thing, but so many things in 5th edition can use a reaction it's kind of nuts.

As for streamline, do you mean streamlining interrupts as a whole? or just or reaction as an action? for the former I have an answer but the latter would need some consideration.

As for how I handle "interrupts" as treating them like declared overwatch, if you've ever played a video game like XCOM, during your turn before the aliens can make a move you can put a soldier in overwatch, which foregoes any primary actions for your soldier, but if any aliens make a shot or try to move within line of sight of this soldier the soldier does something, typically attacking.

In this sense overwatch is an action which is declared at the start of the players turn and is conditional, so instead of counter-spell being a reaction, counter-spell in this instance is a spell a wizard readies and goes into overwatch with it. "If the lich or his minions cast a spell, that triggers my overwatch" everyone at the table knows ahead of time this conditional interrupt might happen.

Though I admit I don't know if this is more streamlined in total, this type of mechanic shows up more in OSR games where reaction actions aren't assumed but some sort of declarative response makes sense.