I just googled "Worst La Quinta ever" and the top result was the MIA airport north property, which looks better* than the Hampton Inn Miami Airport West.
(Actually, they look pretty similar, except that the LQ has external doors to the rooms rather than internal corridors).
I agree though - if there are properties that are so bad that they could damage the program, that would be a risk of integrating LQ wholesale, less so if they were to split the chain into a smaller brand before selling off the more 'challenged' properties.
* - Better because when I stayed in the HI, there was a flight attendant called Howie asleep in the room I'd checked myself into, and that's apparently not a feature of the LQ.