I mean the extra benefit from having double white magic or double black magic only really matters if you're burning through their casts.
Personally for black magic I've never burnt straight through a character's casts except at the early game(at which point this argument isn't pertinent to since can't have a mounted caster back then). The catch for black magic really is if they're male or not to dictate if they can go Dark Knight.
For white magic I'd say it would depend on the unit, having a physic healer with double casts can be useful, also if they have warp and a high mag stat to get the most out of that(though this is only applicable to 3 characters and one of those doesn't get Physic) but the extra mobility can be useful in other situations, particularly if you're using a lot of other high mobility units. There's been a couple of times where I wish I had a healer on Holy Knight so I could get them into position to assist another unit more easily.
The obvious drawback to mounted healers is of course actually training them, you can't be in both a mounted class and a magic class till master so you'll have to get up that riding prof. through group tasks and instruct which can be a pain since you need to get at least near A rank. If you already have the lance req. satisfied through normal play I wouldn't say this isn't quite so much of a problem since that's only one stat you need to focus up but if you've been going purely black and white magic then you'd be putting in a lot of extra work to get them into their mounted class.