I will never get enough of Bilbo handling Thorin's hair... I think it's exactly as you said in the last comment:

Thorin sees the merit in not driving himself so hard (especially now that they have found a cure), and I think he'll secretly come to love Bilbo fussing over him.

OR

We could imagine a lovely AU where mutual hair and beard grooming is part of the dwarven courtship process... yum yum yum.