Nooooooooo. That would only make things way worse, imo, so I will respectfully disagree.
We have enough problems in this country with people feeling they're in a different, lower, class than someone who they feel is doing better than they are, and who may also feel they're doing worse because the other class has a class-based advantage.
So my $0.02 would be to let the liberal progressives continue to try to divide us by class. They've done enough damage with that approach. I don't feel we need to intentionally create a class of citizens that by your own definition, would be second class.