Training makes no sense
It may seem logical at first, but when you think about it, this man CAN'T be trained, not for combat or anything else.
He literally can't learn to react to the unexpected, he can't hone his reflexes, he can't 'become better' at anything, because he never has a 'varying pattern' to deal with.
Think about it, every time he dies, the day resets, so he gets the SAME, EXACT PATTERN! He not only CAN 'cheat' his way out of any 'training sequence' by eventually learning and memorizing every single thing that happens as a consequence of any of his actions (and so on), but also, he's basically DOOMED to 'cheat', because he can't experience surprises or anything new.
It's like playing a video game that always has the same patterns and bosses - if you just keep playing, eventually you will exactly what to do at any given situation, and so, can complete the game at any point you like. It is no longer a game, it's just a test of doing the same pattern in the same way every time - think of those old Laser Disc games, like 'Dragon's Lair', which are barely 'games' at all. You just have to press the correct button at the correct time for awhile, then you win.
This also means, it's USELESS to even DO any kind of 'combat training', because the 'combat' in question will always be reset, and will always repeat exactly the same, so he doesn't even HAVE to learn to 'adapt' or have any kind of 'reflexes' about a combat situation, he can simply memorize and learn, as he indeed DOES the whole darn movie except the end (which makes no sense for different reasons).
Even if he COULD be trained to have some kind of 'intuitive combat reflexes' and to be 'skilled in combat' (that doesn't repeat the same pattern every time), that skill would PALE in comparison to his 'day resetting pattern memorization ability' that makes him PERFECT for every fight (even being able to avoid an angry guy's punches eyes closed).
Would Tom's character be better of being trained for 'hand-to-hand combat' in that situation, or is it just better to use (and frankly, show off) his 'memorization' stuff? He could never do the blindfolded-thing just by bare training, so what's the point of even trying to train him when THAT is what he's doing in combat anyway?
I guess the ending sequence is the only point where the 'combat training' would come handy, if only someone like him COULD be trained.. but how do you learn to be 'skilled', if you can just 'cheat' your way through every single combat situation? All you learn is where the enemy will strike next and to avoid/counter that, but you are not really learning how to ACTUALLY fight and to 'intuitively' avoid/counter those strikes.
The whole 'training for combat'-stuff, thus, makes NO sense whatsoever.