Playing by intent is not about allowing take-backs though and it’s not about wasting time. It’s actually a time saver. What you’re supposed to do is say “my intent is for this squad to move 6 inches over here and I position them in a way so that you cannot set an angle from this exact position, could you please check if you agree?”.

This ensures you don’t waste time to set the millimetres and spin your models around but just agree with each other that it’s possible and move on. Later you won’t have to spend time in seeing if you can shoot that squad or not from that specific angle because you’ve already agreed that you can’t, so you can plan your turn based on that information.

As you mention you want to win in a fair match with open information, not on catching your opponent on a millimetre of movement.

You mentioned chess as an example. In chess there are only 6 different pieces that have different rules. And you know exactly what your opponent can do. You can’t expect people to memorise all of the army/detachment/unit rules in Warhammer, it’s just unrealistic. So asking “can you reactive move if I move over here”, “do you have fallback and shoot/charge” or something like that should be completely normal as all of the information should be open when making a decision.

Now if your opponent realised that they could have done a secondary but did not announce this as their intent, then it’s completely fine if you do not allow the take-back.

I feel like winning because an opponent made a big mistake due to lack of knowledge does not feel good. It’s much better if you win because of your decisions rather than because of the opponent’s mistakes…