It seems like Robin is always well received whenever they introduce a new one. Tim Drake even managed to carry his own book for 20 years. So I think readers accept and like the concept.
I think the Robin role is also a vehicle to show Batman's influence through the greater DC Universe, with Robins usually having a role in Teen Titans as well.
As a concept on its own, I think it works....the Dark Knight's squire and all. I think it works a bit better when Robin is a teenager, though. About 16, I'd say. It's just easier to imagine somebody at that age legitimately being able to kick an adults ass.
That's not to say I didn't think Damien was/is awesome, though. I think that character showed you could do some really unique things with the concept if you have an interesting idea for it.