If a business is going to go bust because they couldn't change their sign on a dime, the business probably wasn't viable in the first place.
This reads like a conservative business owner being annoyed that a government body is existing and doing its job well, which I suppose is a common sentiment.
Also, the LPC has nothing to do with 'progressives'. Its been around since the 60s.
Not a very good example—this kind of regulation is usually focused on preserving the distinctive exterior look of a building, so including the signage in the regulation is not even close to being an overreach, and it doesn't give much indication about whether the regulations do go too far.
Now many of these towns have blocks of buildings with expensive and beautiful signs; none match the name of the actual business inside.
In fairness, so have progressives. (Longer, even.)
Deeming buildings to be landmarks seems like a bit of a mix between progressive and conservative thought.