What if I get cold-shouldered for being overly eager? Wouldn't that be super embarrassing? Besides, there's a vast chasm between my current status in the Jianghu and that of the Lord of the Heavenly Sword Cloud Palace. On what basis am I supposed to welcome him?
On this matter, Feng Yin did have some self-awareness.
However, Bai Changshan and Bai Changhai saw things even more clearly: it seemed that their young princess was opening her heart unknowingly, just shy of voicing it out loud.
If you don't greet them now and it becomes known later that you, of all people, failed to do so, wouldn't that reflect even more badly on you?
Even if you get ignored now and it's a bit embarrassing, once your relationship is established later on, it definitely won't be you who's left feeling awkward.
Besides, with their dear princess present, could you even be humiliated?
Bai Changhai was fully considering these things for Feng Yin's sake.