I think I’d switch that from “quickly” to “eventually”, or “have a head start to” - we could get grid independence “relatively” quickly if the government subsidized it (I highly doubt first Gen fusion competes with natural gas or solar cost-wise), but a large amount of energy is used in transportation, home heating, etc.. Until those become fully electrified you’re still stuck in the fossil fuel economy.
True, I meant "quickly" on a relative scale. One advantage the 1st gen fusions would have is immunity to the supply shocks of fossil fuels and the intermittency of solar/wind. Plus we have workable electric vehicles and every home that has fossil-fuel powered heat by definition has a connection to the electric grid.
It wouldn't happen overnight, but I can think of few things that would kickstart the electrification of everything better than functional fusion power plants.