I personally don't find the trainer battles to be quite boring enough to justify cutting from the videos. Of course, wild pokemon battles are boring as fuck, but at least trainer battles are varied enough to be at least mildly interesting.
In general, it's just a matter of time investment, I'd think. When you look at the playlists, the LPs are already fairly long. Add in a couple hundred trainer battles that have nothing to do with story progression, and that bloats the count considerably. It would lead to quite a few videos being little more than staying in a single route fighting the trainers, with no actual progression made in the grand scheme of the game. It also becomes rather frustrating to commentate random trainer battles--many areas have you fighting the same Pokemon repeatedly, and you quickly run out of random BS to talk about.
It's kind of a mixed bag, I suppose. On one hand, it feels like a waste for him not to show the battles--and by skipping them to do later, he often faces challenges noticeably under-leveled. But at the same time, showing them all really wouldn't contribute a whole lot to the LP experience, and could even distract from it.
