True. As much as I would like to see Rajdhani running from/via BGP, I strongly feel its isn't justified.
Starting Rajdhani from BGP isnt possible due to it not being capital of a state. Logically thinking, Rajdhani passing through Bhagalpur wouldn't be suitable too as it will take a longer, but much slower route. Moreover, seats available too wouldn't be sufficient. Leave the Rajdhanis as they are, so as to preserve their Status .
The best solution would be to start a...
more... LHB AC Express (of course after expansion of yard), which will provide ample seats for people of the nearby region. And as Manish Bhai pointed out, stoppages should be strictly limited- JMP, PNBE, MGS and CNB (Kiul for Loco Change and maybe ALD too).
Giving another rake to Garib Rath would be quite helpful too