Actually 1 and 3 are same points.
Since Gorakhpur is the shortest route between Patna and Delhi and Patna Rajdhani is totally full during normal times, there seems justification for one more Rajdhani.
Here Railfans aren't demanding extension of some other state's Rajdhani or diversion of existing Rajdhani. They're simply demanding a new service from the rakes that would get freed after converting Patna Rajdhani into Patna Tejas Rajdhani.
Dibrugarh...
more... and other potential North Eastern Rajdhani are just Lollipops of existing Bihar based Politicians to gather votes, some want via Bhagalpur or Jamalpur or Purnea or Saharsa or Darbhanga or Narkatiaganj or Raxaul or whatnot.
They're simply doing only thing they're good at- stupidity.