When the Senate Parliamentarian says that Republicans can't enact their policies (2001, Bush tax cuts): Trent Lott fires the Senate Parliamentarian and finds one who says that they can.
When the Senate Parliamentarian says that Democrats can't enact their policies (2021, minimum wage increase): Chuck Schumer does nothing, Joe Biden issues a toothless statement expressing his disagreement, and Kamala Harris says she won't override the Parliamentarian's advice.
If Democratic Senators wanted to increase the minimum wage, they could. That they aren't doing so means that enough of them don't want to, despite its high approval among the public.
Do you think the parliamentarian is wrong about procedure, or do you think she is right about procedure and should be ignored anyway?
I honestly do not know. I have not looked enough at the issue to know whether the policy proposed fits within the rules of budget reconciliation. I do know that Sanders, as chair of the Senate Budget Committee, requested a study of the matter (whether from the CBO or the OMB, not sure) to illustrate that raising the minimum wage impacts the federal budget.
What I do know, however, is that all this would be avoided if Senators actually cared about the arguments Hamilton and Madison made about why supermajority requirements for ordinary legislation are bad.
And I also know that the general public won't give two shits about what the Parliamentarian said and will punish the Democratic Party for not raising wages when they said they would and had control of the House of Representatives, the Senate and the Presidency.
EDIT: That is, whether or not the Senate Parliamentarian is right about procedure is irrelevant, because the procedure shouldn't need to exist in the first place, and it's bad politics anyway.