Combat training is one of these cards whose efficiency is kind of doubtful but I like using it anyway. Compared to other standard permanents it really isn't very good. It only costs one less than a Helicarrier, but a point of damage is much less useful than a resource, and it only gives you that point of damage on turns where you use your basic action to attack, meaning it does not work on turns where you thwart, or defend, or recover, or use an action to remove an attachment, or are exhausted by an encounter card, or exhaust to remove an obligation or perform any other effect. That totals up to quite a lot of turns where you can't use it. Some characters have ways to attack more than once per turn and thus gain more than one damage per turn from this card, but except in the very strongest cases this doesn't really happen often enough to fully overcome all the turns where you can't use it. And characters who are extremely good at making multiple attacks per turn also tend to have high thwart values that make you want to double thwart instead of double attack.
Nevertheless, having another power up permanent in your deck can be handy, and it is just fun to permanently improve one of your combat statistics and permanently become a more powerful attacker. And you could be casual in when you play it, ignoring it if you don't have the resources for it, or playing it when you don't need damage so that you have more damage when you do need it, or maybe you can wait to play it cheaply with Power of Aggression.
Generally you want to give this card to a character who never thwarts or defends, only attacks. And having a few cards that let you double attack, like One-Two punch, is a nice plus. Or you can give it to a character like Captain America who usually thwarts but has a decent attack and is extremely good at making multiple attacks per turn, just because it is fun to give him a balanced 3 ATK and 2 THW and give him more interesting tactical flexibility.