Mat has all the above and more (incl. charisma) - no one is better than him in all the above, IMO. The likes of Bashere and Rhuarc have deferred to him before, so did Seanchan field commanders in KOD - and Rand, who knows better than to think he's a military genius. Mat will just need underlings good in all the above, to advise him and implement his decisions. As for politics, if he still needs that much during the War, the Light won't be in good shape anyway. We've seen what he could do in politics with his face off with the Sea Folk anyway, or how he handled Tuon, or how he acted with the AS when he left Salidar. He has it in him (as Trcikster but also from his memories), it's just not skills he had to use prominently so far.

His greatest challenge would be channelers, but we've seen him improvise rather well with those in KOD, and no doubt he has great experience of facing dreadlords and fighting alonside Aes Sedai from the TW. He just needs to learn more about WOS-style warfare.

Mat would be totally wasted as a field commander, he needs to handle the big picture. He wouldn't last long against the likes of Taim with a strike force (Demandred is clever enough to know to stay out of the field... his behaviour/comments at the Cleansing showed this.. he was the brain behind battles, not the muscle) - and he's much, much too precious to risk losing that way. He's the best strategist the Light has, and militarily he's their best hidden ace. He has so many generals in him he's the most unpredictable commander/strategidt imaginable. He doesn't have patterns the way an Ituralde, Bashere, Demandred, LTT have - he can fight like one general one minute and like a completely differently one another. And unlike LTT, Demandred doesn't know him, and even if he comes to think he does know him or figured him out, his 'style' etc., he still won't know him for real, because Mat will still have many other generals in his head Demandred has not yet seen.

A lot of what you assign to the Captain-General would actually be the charge of his general staff anyway. Some Seanchan would be excellent to work lines and supplies and with organization... placed under Mat they'd be killers with this, especially if you 'upgrade' them with Travelling and they can do their stuff with that instead of to'raken. The clan chiefs know best how to lead Aiel, Bashere and his officers are best with cavalry etc. yet Mat understands all of what they're doing. Mat could probably even teach the Green Ajah stuff they've long forgotten about their TW strategies/tactics, weaves asidde, and LTT knows stuff they have no idea of from the War of Shadow. A lot can be passed, hinted at then practiced via mixed circles's teaching.

My feeling is that the time to risk Mat in the field once TG has started, if the Light is wise, will only come when it's time for someone to lead the forces fighting around SG while Rand and others strike at the Bore. Then it would be time to place Mat in the field. I would even say it's likely end in disaster if the Light let Rand engage in war elsewhere against Demandred beforehand and uses Mat just as field commander without putting him in charge of the greater picture. Only Rand can devise a plan for the SG strike, so it would be really stupid to risk wasting him against Demandred in the field. When he had him, Rand has preferred to rely on Mat with Bashere, Rhuarc and co. anyway. At the moment, Rand can be a great fighter for duels and such, but as General he is still fairly poor on his own.

IMO, there will be just one massive battle Mar will involved in in the field, the one that launches TG. Then, the fighting will spread everywhere and Mat's job will be to coordinate all this until the time of the strike comes and he will take the field again.