Shift right is so necessary for the oligarchs stooge, because if you created a new wholly neoliberal party from scratch, nobody would vote for that obvious trash.
So, what they do, is they find a light socialist party and seed it with insertionists, lobby stooges etc, even college age ones. Completely undermine authentic politicians.
They gradually take over said socialist party, kidnap their voter demographics, hold up the far right as a dire existential threat as often as possible.