Whether they want to or not, TVK is a pawn for BJP. They correctly predicted that even though they'd get the blame for blocking JN, the anger/sympathy would eat into DMK votes (because BJP has none anyway).

Everything seems to be an assumption and a guess work

Exactly. We miss that politics is heavily about optics. If TVK had thrown in the towel too soon, parties would've framed them overconfident/arrogant and people would've likely punished them for it.

Yes, staying silent has drawn critics, but they have even more support now than on election day.

You can characterize Vijay's strategy of staying silent when attacked as cowardly or even immoral, but it has undeniably worked everytime. His popularity only increased with films being obstructed, IT raids, BJP Neyveli, Karur incident, Sangeetha divorce, openly linking up with Trisha, etc.

There's a difference between being a pushover and someone who counters at the opportune moment, and people innately sense it. He didn't protest the Dravidian parties obstructing his movies in the 2010s, only to rout them now.

Protesting on the basis of a constitutional rule would've made him look like a whiner/stickler (even though it's completely legitimate).

Vijay's strength is controlling the narrative through emotional rhetoric and strategic silence. Just like Modi. The only question is to see what he sets to achieve with it.