I prefer the looser casting rules because they allow the narrative to be more flexible. Going back to the counterspell example, having one player able to counter another's counter is fun, and allowing casting times to be flexible (which to me is more logical anyway, but that's besides the point) permits the story to keep moving and make sense. For me, story always comes ahead of mechanics, so my priority is maintaining a narrative that is fun and makes sense, and if the mechanics are interfering with that, then they gotta give.
I tend to hand wave a lot of stuff at my table. Like, if a player wants to try something that is outside RAW but seems like an awesome idea that will take the story in a fun direction, I am inclined to go with it and see what happens. Instead of "that's not really how charm person works, sorry," I'll probably say, "huh - that's creative. Let's see what happens!" Within reason.