These are just examples to show what I mean, rather than actual considerations to be made on how this could be done.
Maybe her heal is greatly reduced when used twice on the same target.
Performing abilities from a new teammate, could reduce the ultimate cooldown by X seconds (can only occur at Z minutes, per champion)
There are probably much better solutions to this issue, however, whether she should be rewarded for switching OR punished for babysitting a champion is a design choice from riot games point of view. Maybe a combination of both would be the best solution.