Back in BG 1 and 2 the Bhaalspawn were ever race, anyone and everyone could be a Bhaalspawn. They did not have dragonborn back then but they'd have had them be a Bhaalspawn too.
Due to that lore wise the dragonborn makes sense.
Hardly.
In the times of Bhaal dragonborn did not exist at all. And even now they are extremely rare and made up mostly out of people from a single city state from a world without any gods and a tiny handful of holy warriors of the platinum dragon.
They stand out so much that commiting a murder as a dragonborn is very easy to track back to them if there is any form of witness or evidence.
Likewise it makes 0 sense that dragons, especially evil ones, take the form of dragonborn because of their association with good dragons, the race being only 100 years old and some probably not even knowing that dragonborn exist and dragonborn generally being very hostile towards dragons.