I am not advocating about slowing down combat for the QTE, the combat would take place at the same speed and you could toggle a button at any time to trigger reaction right after the enemy turn. Sure it is a small window, but it would be the less intrusive way to do that without automating or slowing the pace of the game.
Ignoring the real-time elements in a turn based game issue, how do you imagine it being implemented without slowing the combat down. Let's keep it simple - attack of opportunity. Enemy leaves your control zone and you get an opportunity to perform an attack against him. As things currently are, an enemy likely to already leave your control zone before camera pans over (it's a problem in itself, but anyway).
So we need couple things:
1) make sure the player has a clear view on the situation
2) Focus player's attention on right actors: clearly communicate which enemy is moving, what reaction we have an opportunity to perform and by which character (there can be multiple player characters engaging the same enemy afterall)
3) after that give a handful of seconds for player to react or not
4) then the enemy continues to move away, or we switch to the next character who can perform a reaction
The reason it would need to slow the game down, is because the player doesn't have control it - yes, some reactions don't require much decision making, but some will! Especially those that consume valuable resources, like spells. Using a reaction is a big deal - it can not only waste 1/3 of your per-turn action economy, but also consume resources that could be used later in combat. By making it a QTA, you need to give EVERY reaction enough time for players to analyse the situation, otherwise it would be actually worse then what we currently have - both not really allowing players to control what is happening AND potentially making players miss out on them entirely. That IMO MUCH worse, then a popup that can be dismissed when player know he doesn't want to use reaction, but gives him unlimited time to check his resources, check him or enemy stats and weight the ramifications of the decision.
And that doesn't touch a hell that would be if one QTA would trigger different reactions - lets assume we have multiclass warlock with rogue. We get hit and can either use uncanny dodge or hellish rebuke. How do you do that? (how the current system would handle that with both on? Roll dice between the two? Pick helllish rebuke cause offensive way is Larian's way?)