You will only need enough storage to cover 12-24 hours to reduce that a lot: Much of the surplus power can be put into vehicles when they're resting at home overnight, or for evening and next morning peak.
For the rest, well, so what? Temporary "oversupply" on days when there's lots of sun and no vehicle to charge up is not the worst problem to have - it won't kill anyone. The worst that you can say about it is that it's a misallocation of resources to sometimes have the power supply that you can't use or sell. But solar panels and batteries are becoming cheap. So the upside of having occasional surplus remains, the downside diminishes.