That's what I considered doing since I did have an initial light up there (meaning I had power up there somewhere), and I actually found a hole that lead up to the area that someone must've drilled to run wires but never used. What worried me was that I would be forced to essentially toss wires across from light to light with only being able to tack them down right by the next light. I'd have to check NEC to be sure, but I know that for wires in the wall, they're supposed to be tacked down about every 2 feet and within 12 inches of the box. I could easily do the latter (just stick my arm up the hole), but I could never secure the wire between the lights.
Fortunately, the kitchen is only about 12'x12', which isn't really big enough to need recessed lighting. The reason why I wanted it is just that it's more modern, and it didn't seem sensible to update everything except for the lighting. However, I am changing the older light out for something a little nicer, so it will still look good. I'm also changing the super old light above the sink to a nicer pendant light, so it's fine.
The kitchen has one advantage in that it has upper cabinets, which can be used to house the power supply. The transformer that I linked is going in the upper right cabinet, which is where the conduit was run through. I'd prefer that it wasn't in the cabinet though. The problem is that my ceiling isn't that high (about 8 feet). So, the crown molding that comes off the cabinets actually goes all the way up to the ceiling. If I had higher ceilings, I would've been able to leave a space above the cabinets, and I would've put them on the top. In that case, the crown molding would've hidden them from view while leaving me able to access them in case of an issue.
For you, you could consider putting the power source in a bathroom base cabinet. You'd have to hide the wire going up (I assume the lighting is up higher since it's main lighting), but you could do that with some trim. The only negative about putting it in any cabinet is that these things do get a little warm, so having them in the open but out of sight is definitely preferable. If you have anything in your bathroom like a linen cabinet (those really tall ones), that might not be a bad idea either. Also, perhaps if you have a non-recessed medicine cabinet, that may have enough room on top to place the power supply given some trim to hide it.