Personally I've never come around to their side of things, although I do recognise the inconvenience of charging cables while you are using a peripheral (Apple Mouse charging port location especially :D )
1) If the device battery is dead, I can swap it out in seconds and be up and running immediately.
2) Built-in batteries fail, and replacing them ranges from difficult to near-impossible and often involves damaging the device's casing to get the built-in battery out.
When I'm spending $100 on a computer mouse, I'd really like it to last longer than the life of the battery and not have to destroy the casing to get to the battery to replace it.
Now you have the best of both worlds: Economical rechargable use for the 90% of the time that the user's in their normal routine, and easily ability to swap temporarily to universally-available alkalines in exceptional situations.
Note: When I had one of these, I just used my own NiMH AAs and jammed a folded-up piece of cardstock against the detection switch, which worked perfectly fine.