All of mine are the same as Rigsby. When I first got them, I bench tested them, and if left long enough on a USB charger, the blue light eventually did go out. But I've never seen that happen in any of the cars. I think the battery just never reaches full charge on the average trip. Either way, don't worry about it unless you find the camera shutting off w/o shutting down properly - in which case it's a shot battery.
On a side note, I had been using Sandisk 64g class 10 cards from day one. Once a week a random camera would power off (blue light only). I'd have to reformat the card for it to stay working again (for another few weeks). I've since changed to Lexar 32GB cards in one vehicle. It's been over 3 weeks and not one camera has acted up. I really think a lot of the gremlins people have with these cameras are incompatibilities with the microSD cards.