But the party can see when voters leave their party and register with other parties. They can see people fleeing the Democratic Party and registering for parties like the Green Party or the California Peace & Freedom Party or just registering as Independent. They have access to this data. It sends a message.

That's not a problem that's a feature

True but this process only works to a point when they've lost so many such voters that they keep losing elections the more centrist/right they go. I think we're somewhere around, perhaps just past that point as of the last prez election. Once that crisis is reached, either it's handled internally by alternative ideas - like running leftist candidates, or externally by having independent leftists candidates beat D candidates in elections. If Trump's admin wasn't such an abject failure at delivering what it promised, we probably wouldn't be talking about D midterm wins. A midterm victory would prolly give a false sense of recovery for Ds but should they continue business as usual (and they likely will) we'll be back in crisis soon after. Perhaps not too dissimilar to Kier Starmer's approval trajectory.