Food for thought: we should be training thinking too, and that's why soft/slow sparring is underrated.
What am I on about with that headline? In all martial arts and combat sports, you drill techniques, which is boring, but very much necessary. In some martial arts, and all combat sports, you also spar in order to train for “real fights” or “the street”, because being able to act under pressure is necessary. But a lot of schools/gyms just assume that if you drill a technique enough, you will eventually be able to apply it under the pressure that exists in sparring or a fight.
However, I think that this is inefficient at best and wrong at worst. The reason being is that in such a fight situation, your brain is not able to think all that well, so you resort to a select few very simple techniques that you're very familiar with. So what you end up with is a fighter who knows a bunch of techniques well, but in the context of a fight, their brain is just unable to apply those techniques to the situation.
Of course, you can brute-force your way past that point by endlessly drilling a wide variety of combinations for the same technique, so you can do that technique very well and execute it starting from a wide variety of situations/positions, but I think it's more effective to train the thought process instead (or as well).
How would we do that? By soft/slow sparring. So instead of going into the round, giving it all you've got and trying your darndest to land as many hits as possible, calm down, both of you. When you need a moment to think, pause the situation. Allow your partner to pick up on openings, and use them. And because your partner does the same for you, you'll be able to stop and think for a moment: is that familiar technique you're about to attempt really a good option here, or is it something you'd have to use a lot of force for? (Specifically thinking about throws/takedowns and how, for example, it's very inefficient to try to throw your opponent backward by force when they're already hunched over forwards)
When you don't train your brain to think this way, don't be surprised that it can't think this way under pressure.
I'm not claiming I came up with this line of thought, I've seen it in discussions on Youtube and the like, but I do feel like it's something many schools/gyms haven't put into practice.
Personally, I do Jiu-jitsu (not the Brazilian kind), so that's just the background this is coming from. For people doing sports with less variety, the benefits may not be as pronounced. Also, I'm using “sparring” to refer to any kind of training where the techniques aren't pre-defined and the opponent is somewhat resisting, be it for grappling or striking arts. I decided against using the term “rolling” because we don't roll on the floor.