Size of the starter needed for the batch size and OG is one reason. I can make a significantly smaller start with a stir plate than without. I can also start it late at night the day before I brew, and it will be done/ready before I am ready to pitch the yeast (about 24 hours)... I can also go to work with it going and not worry about someone not being home to swirl it during the day (I live alone). If I'm brewing on a Friday after work, then this is vital.
So time for a starter to finish is another factor. Where yours takes 2-3 days, mine takes <24 hours on the stir plate. That's with a month old (or older even) packet of yeast (Wyeast Activator pack). I do use yeast nutrient in my starters, which helps (but you can do that too, so no difference).
Of course, there IS the 'coolness' factor of a stir plate and flask setup. Just look at it as a 'one time buy' type thing. If you're able, make one on the cheap. If you don't have the time (or the tools to do the job), buy one. I bought mine and couldn't be happier with it.
Something else I've been noticing lately... The starters I've made via the stir plate seem to have less lag time than those from before. The last batch I made had less than 7 hours of lag time (it was fully active when checked on 7 hours from pitching)... More starters/batches will help to determine if this is universal, or just a few odd batches.