Actually, US airlines failed in maintaining a LCC (Ted, Song, etc) and decided to compete on pricing on same hardware with other LCCs. Not run a LCC as part of mainline.

Air India Express is maintained separately to compete with Indigo on the same routes Air India also has full service flights. Mixing the two under the same name results in consumer confusion when some flights offer full service and some are no-frills on the same route. Or they have to significantly discount even full service when there is competition like US airlines do. So, at the minimum, branding being different has good reasons behind it. Two different hard and soft products in parallel. Not like regional carriers supplementing mainline as feeder airlines.

That leads to two different HR organizations where one pays less than the other commensurate with price and cost structure. Different contracts even if there is some mobility between the two.

The only thing left to integrate are their loyalty programs which they are trying to do.