No, Paine is an OG, he's fine.
It is more that if somebody says "X is common sense" it is not really a statement about X but rather a statement that "(not X) is not common sense".
If you look at the names endorsing that document the first one is
https://en.wikipedia.org/wiki/James_Carville
who was associated with Clinton's winning 1992 campaign and the losing campaigns of Kerry in 2004 and the other Clinton in 2008 and other people to the right of the Democratic party. It's true that this contingent can point to a few presidential wins but both Clinton and Obama were accompanied with a long-term erosion of the Democratic presence in congress and especially in state houses -- a time when Democrats have been winning at fundraising and losing at everything else.
Jurgen Habermas points out that a viable political system has to have public participation but also expert guidance on many issues. For instance, AI, advanced manufacturing, and climate change all require more than "common sense" to get on top of.
It would be good for the Democratic party to agree that cis lives matter, stop using words like "LatinX", etc. That document is not saying though that the Democrats should make a break with long-term trends that have eroded people's trust in institutions.
I feel like most of my exposure to the term "common sense" has been people trying to justify with rhetoric positions that don't actually stand up to detailed logical discussion.
The "expert guidance" thing is an interesting point, our american system seems to make the existence of this dependent on the whims of the executive who is elected for completely unrelated issues.
I suspect that if you presented a simple poll question: "should donald trump have (more?) expert guidance available", the vast majority of people would say yes.
Of course, donald trump is famously not someone who would ever try to get access to or listen to expert guidance and everyone voting for him knew this and he was still elected.