This Chalukya express was meant as a dedicated train for Mumbai Bangalore passengers. Extension of 3 days to Tirunelveli and 3 days to Pondicherry itself was a foolish decision, taken to appease Karnataka private bus operators. Just see the pathetic timings and of this train in SR/ SWR Stretch.
To cater to Thiruchendur, Tenkasi and Tuticorin, SR should introduce a train. Not depending on CR or spoiling an already spoiled train.
In my view, SR's NCJ CSMT should run daily via MDU SA KJM DMM GTL SUR...
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PUNE.
Triweeklies should start from TN and TCN covering North TN route MDU TPJ VM KPD RU GTL SUR PUNE.
If SR is willing, they can run a bi weekly via SA UBL route.

More than Bangalore (which relies on Udyan and LTT-CBE), this one was more of a lifeline for interior Karnataka to reach Mumbai or reach Bangalore by night. NW Karnataka got UBL-DR later on, rest of the section has not been compensated. Bangalore needs a SF in this route with convenient timings at both Mumbai and Pune.

The General Quota for this, I think starts from Dindigul/Madurai (when it enters Madurai division) from where onwards the train starts emptying steadily and an extension to Tiruchendur would give an option to pilgrims...
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to travel using the berths vacated by passengers from Mumbai/Bangalore.

Bangalore Mumbai had 3 dedicated trains and a passing train.
Kurla Bangalore was extended to become LTT CBE. Then Chalukya was extended. Udyan was handed over to CR and made as a fast passenger.
Apart from this, daily Train of SR Cochin/ Mangalore to LTT was running via KJM pre Konkan era. Now vanished.
Pre covid era, 4 days a...
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week NCJ CSMT (SR train) was running via KJM GTL route. After covid, now it is going via KPD Madanapalli completely avoiding SWR area. Compensation to Jayanti for KPD. Loss to Bangalore. See it's speed in down direction now after KPD till NCJ - very slow.

In my opinion, railways should restore all 3 trains back as Mumbai Bangalore trains operated by SWR. Southern Railway can run their trains from TN towns.

I am not going to refute the facts you have pointed out regarding Bangalore.

The 11302 Udyan is obnoxiously slow (just as 11013 LTT-CBE, in the opposite direction) and you can't pinpoint the issue to one specific zone.

No...
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explanation was given for 16339/40 or 12649/50 rerouting which were blatant robberies from Bangalore passengers. Bangalore deserves a dedicated daily SF to both Mumbai and another to Delhi (via the shortest route) as a bare minimum.

Chalukya, they extended because it also solved the issue of Bangalore connection for Pondicherry and Tirunelveli back in the time, and only one additional rake was needed. Same was done for LTT-CBE further back, but now it's back to running with 3 rakes.

Some well-patronized trains from other zones (Sanghamitra, Seshadri for example) were extended to Bangalore as well.

As far as my rationale regarding Tiruchendur extension for this one, this is purely keeping in mind the intra-state passengers in Tamil Nadu (there is only one Chendur Exp with reserved coaches which is an overnight train) who would benefit.

A good number of passengers deboard in the DG-TEN stretch (at least half the train gets emptied at MDU due to the General Quota) and they are not replaced as the TPJ-TVC Intercity is operating right next to it in both directions.

It's not a case of taking a train bursting in capacity and burdening it further. This would be the equivalent of extending Hampi/Gol Gumbaz/MYS-KCVL/MYS-KCG Exp to Chamarajnagar (which has a lone crawler train to TPTY beyond MYS while most of the crowd for the trains I've mentioned for example here, empty out at Bangalore itself).

As I've said before, those from Tiruchendur (not a huge number if you consider TEN, VPT, MDU, DG stations all constitute General quota) who want to travel to Mumbai/Bangalore, they would not have much problems boarding the train at Tirunelveli in any case.

SR is unbothered to fulfill the bare minimum, that is restoring its crucial trains of the MG era (those running entirely within its limits, like the CBE-RMM Exp), it'd be a long time before they would get to the point of exploring the routes you've mentioned.