Yeah and it would justify the existing cost of the pager in the first place, a sort of "well of course it's expensive for the convenience!" sort of thing.

But mostly it'd just be cool. Because how cool WOULD that be. And like I said, since the ride pokemon would have like saddles and stuff on them, it would make sense if they CAN'T battle (and would be very put out and/or leave if you tried to make them) since that stuff would get in the way.