Only if it could be done in an apolitical way, which seems impossible in the current political climate. The legitimacy of the US Federal Government depends on the perceived continuity of the (now mythical) constitutional order. If one party or the other packs the court without bipartisan support for their nominees in the Senate, it would be denounced by the other as an authoritarian end-run around the constitution--as a revolutionary rather than a mere procedural act. IMO this would be more likely to foment disunion than it would be to restore the bygone constitutional order.
The fabrication of legitimacy is indeed the main task of the supreme court.
However violence is another way to project legitimacy. Putting someone away for life or drone striking a goat farmer provides real legitimate proof of power.
The government is much stronger than it was 100 or 200 years ago. So perhaps it can dispense with appearances of judicial legitimacy using the currency of violence. It's not clear they need to continue with the fiction of an impartial court to hold their grasp; like a space ship they can jettison that hallowed out rocket having already safely been placed into orbit.