Its not necessary Rajdhani should connect capitals only. Have you not heard of New Delhi to Bilaspur or Dibrugarh Rajdhani. Are Bilaspur and Dibrugarh capitals???
The idea is that they connect capital cities only. BSP Raj was run till Bilaspur due to lack of facilities at Raipur. Dibrugarh Raj was run for the benefit of the passengers of the North-Eastern states like Tripura, Mizoram, Manipur etc who did not have any rail connectivity to the rest of the country.These exceptions were introduced because of constraints specific to these cases.