If he were actually casting them via the Planar Touchstone feat, then they would be limited to 1x/day. Since he's instead scribing them into his spellbook, they're just like normal spells to him.
You could just ban this whole thing, since I've seen some pretty decent arguments about how it's not really 100% legal. However, as X-codes said, it really isn't a huge power-up, since wizards already get most of the good spells, anyway. (And there are other ways for them to steal spells from other lists already, like Recaster, Wyrm Wizard, etc).
In a way, it may make him a bit
weaker, as he can take the place of the party "healer"/cleric, but if he does, this will require a fraction of his daily spell slots. (OK, overall he won't be
weaker, but it may spread his resources a bit thinner).
What you should be more worried about is if he picks up Uncanny Forethought, or some other way to cast his spells spontaneously.