Sir, I agree that intra state connectivity in Karntaka is of prime importance and the state capital certainly needs to be connected well to all parts of the state and there indeed is a lot of rush to either coastal karnataka(Which Railways still arent able to serve properly due to HMRDC and ghat constraints) or north karnataka.SWR should certainly prioritize that.
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Having said that, KA shares a very close relationship with erstwhile AP, now the two states of TG and AP, economically and culturally, Hyderabad Karnataka depends on Hyderabad for business and...
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so do most parts of North eastern KA bordering TG and AP. Similarly Bellary belt on areas extending upto Guntur and Krishna districts in AP. However, SWR, apart from BZA-BNC/UBL pass, SBC-HUP pass, UBL-SC daily exp and YPR-KCG tri weekly express, couple of trains to tirupati does not operate any trains to any part of AP or TG except passing trains(Maybe a few more that i missed like kuppam MEMU). SCR on the other hand runs SC or KCG to GUR/BIDR/BJP/RC daily passengers to all around north hyderabad, TPTY-UBL pass and even the recent SWR section trains in kalyanadurgam, almost all trains between KCG-SBC including specials to KJM, BZA/MTM/CCT to SBC, trains from VSKP are operated by ECoR.
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All I am trying to say is, SWR is running one special to VSKP which also is a major crowd drawing city to BLR and unlike many other states upwards has a significant amount of KA based businesses and interests too. And the rake perhaps can be made small and along with a few coaches drawn from the umpteen number of trains SWR runs to various other places/zones (which have sufficient capability to run their own rake if required to SBC like SCR does) should certainly run a special and once doubling between TK-ASK is done should even regualarize it.