Well, the thing about the wings is that you can use a bonus action to manifest them and put them away. They don't have to be out all the time.
I was actually a little bothered by the wings appearing and disappearing, but then I thought about how many celestials and fiends have the ability to alter self and appear as normal humanoid and it makes more sense.
It makes a little less sense for the draconic bloodline. For them the wings should be either permanent, or their entire draconic appearance should be able to come and go (I personally prefer the second option). Of course the sorcerer can always get the Alter Self spell, but that only lasts for an hour and requires concentration.
In addition, they don't have to be just angel wings or bat wings. They can be wings of metal, like Archangel from X-Men, or wings of energy like Tyrael from Diablo, They can be concentrated energy propulsion like Starfire from Teen Titans... really you can skin them as anything.
Re-skinning is certainly a thing you can do, but a default angel or demon wings is a good baseline.