During British rule, Capital/ head quarters, where the British Officials resided was every thing to Govt. and other population centers had very little importance. The same mentality of giving unduly high importance to HQ/Capital is still continuing with present day Govt and also amongst the Indian citizens to some extent.
Concept of Rajdhani Express was introduced in (NDLS-HWH) 1969 as a strictly overnight premium train and second Raj i.e. NDLS-BCT was introduced in 1972. At that time there was no ACIII class; berths in ACII & ACI were prohibitively costly to even upper middle classes and Raj was a meant for politicians, bureaucrats & rich class. Still Most of the coaches in Raj used to be ACC which were not comfortable...
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for overnight journey. Upper middle class normally used to occupy these ACC in order to enjoy these privileged trains. I still remember my childhood sight of Mumbai Raj for the first time from fields at outskirts of Bhayandar, which was probably biweekly and had only 9 or 10 coaches in may'79.
So historically, Rajdhanis were involved with only top 3 cities of India. Chennai was excluded as ACC journey from NDLS-MAS is not practical.
Today scene has totally changed. Reasons are advent of ACIII, increased purchasing power of people and lesser increase in the cost of ac travel than general inflation. More over, Tier2 & tier3 cities had grown up financially as well as demographically.
Literal meaning of Rajdhani should not be given undue importance. Rajdhani is just a premium class of train which is given high priority during its run and should be meant to run between destinations where it can earn enough passenger response/ revenue. Why it should be limited to Delhi only? is is meant only for the MPs/ MLA etc only who travel free or for the public also who pay and travel? Today around 100 Rajdhani trains can be introduced without having Delhi as one of terminal destination.
Once the upgradation of track to 130kmph+ speeds expands, we can see Rajdhanis (or Rajdhani type trains) with 80kmph+ avg. speed proliferate through out the length and breadth of IR network.