Everything depends on actual implementation. In healthcare, for example, we already had a system where state money was sent to private healthcare and pharmaceutical companies corporations. The problem was that the poorest people still had trouble getting covered. This proposal would have broadened the scope of who can afford that by providing poorer folks with direct government subsidies for coverage. Nobody is calling subsidize childcare in Scandinavian countries a "right-wing policy" because private providers exist.

Lowering military spending by aggressively shrinking active duty troop levels and eliminating weapons programs is certainly left-wing. Raising income taxes on the highest earners and raising the corporate tax rate have always been associated with left-wing policies in the US.