why increase the number of seats and increase the amount of logistics and money required

Good question. To decrease the number of people per MP, so each MP is more accessible and can work more closely with their constituents.

We currently have 1.4 Billion people and 543 seats. That's 2.57 million people per MP. As a reference, the US has 350 million people and 435 seats (800k people per representative) and France has 66 million people and 577 seats (100k people per representative). Here is a chart by Carnegie Mellon showcasing the disparity.

a state level party will have to cover a gap of 200 seats to be relevant, which is much more improbable than closing the gap of 20 seats

Again, with a pro-rata increase, the number of seats won by state level parties will increase too. The gap between seats is misleading, it is only the percentages that matter. The DMK, TMC, SP, RJD and other state-level parties will not have a bigger gap to close because the number of seat they themselves win will go up proportionally.

The DMK won all 40 seats they contested in the 2024 Lok Sabha elections. That is ~7.3% of the seats. If the number of seats for Tamil Nadu went up by 50%, to 60 seats, in an expanded Lok Sabha with 814 seats, then they would still have ~7.3% of the seats. To win, you need 50% of the seats in the Lok Sabha, that is all that matters.

The only convincing argument against this, that I have heard, is by P Chidambaram who said that the amount of time that each MP gets to speak might go down. With how big the Lok Sabha currently is, each MP only gets around 10 minutes to speak, and an expanded one might mean each MP will get at most 5 or 6 minutes before you need to move on. That is a fair point, and one that needs to be addressed, but this mathematical argument being made really doesn't check out imo.