No, most leftists don’t say that, but it isn’t because their policies don’t support that ideology, but rather, they are ignorant of where the polices they support ultimately lead.
I have said this many times, but it is worth repeating. Immigrants who have escaped Comminust countries and were not part of the Communist Party that come to the US are ardently opposed to the Democratic Party. They start with a clean slate as far as US politics go and they are able to see that the Democratic Party most closley resembles what they escaped. I only wish Democrats moving from blue states to red states were as wise and would stop voting for the same nonsense which forced them to leave their home states for the greener grasses in the red states.