Buffalo and Rochester Mayoral primary results suggest otherwise. Two powerhouse NY Dem. Party Mayors, very "tough on crime" and business-friendly, just collapsed to Democratic Socialist candidates.
Lovely Warren is under federal investigation and her husband is a drug dealer. She had no claim to being "tough on crime" except insofar as she was willing to cover up police malfeasance that reflected poorly on her running riot of an administration. She was, in virtually every respect, the opposite of a law and order candidate.
The Buffalo election appears to have more in common with AOC's victory over Crowley: An energetic, talented challenger winning a low-turnout primary against an assumed-safe longtime incumbent who didn't even bother campaigning, and whose power had come to rely more on his enmeshment with powerful actors within the Democratic Party than with any kind of relationship with his constituents.
Brown also has longstanding corruption issues - including abuses of power like coercing donations to his campaign from city employees and intimidating volunteers for rival campaigns..