I'm from Kumta, KA & I always see this train. The demand is crazy high. The train is almost packed by the time it reaches Kumta/Honnavar, and don't forget there are big towns like Udupi, Byndoor, Bhatkal, Kundapur, Murudeshwar, Surathkal up ahead.

According to Railway rules, the starting station gets the General Quota, they can't change that and give other quotas. The quotas you mentioned apply from the middle stations.

There's also a bit of tension over revenue sharing between the different Zones. The starting stations get more money, then the ending zone. The middle/passing zones get less.
When it was introduced hastily, the train was running as an UR Special between Karwar - Vasco - Karwar, because at that time the new platforms at Madgaon were still under construction. KR also makes some money for maintaining/cleaning/watering/fueling & other upkeep tasks. If it were to extend to Vasco, KR would lose the money from terminating there + more. So, KR is also not too keen on sending it to VSG, SWR.
The same goes for the Mangalore-Madgaon Passenger, Mangalore-Madgaon VB or the old Mangalore-Madgaon Intercity. They never extend it even when there isn't a single train from Vasco heading towards Mangalore or the South.

On the flip side, VSG, UBL Div, SWR don't really want to accept it either, since they have a ton of Freight traffic running to or from Murmagao Harbour and all their lines are always busy.

Fun fact - 15-20 years back, when Madgaon only had 3 platforms, they struggled to handle trains in the afternoon. The Mangalore passenger, Janshatabdi would arrive around the same time and they would have their turnaround there. So, KR just extended the Mangalore passenger to Verna, a small station under their own control, instead of the popular Vasco town.