You're making a lot of assumptions. Size of roof, type of solar installation, climate, geographical location, how much the person drives, whether electric heating is resistive or uses a more efficient heat pump, whether their house is well-insulated, how much hot water they use: all of these effect whether or not someone can achieve an energy surplus or not from solar.
It's quite possible for someone to produce enough energy for their regular use from rooftop solar, even if they drive an EV and don't have natural gas. If they're using an electric resistive furnace to heat a large, poorly-insulated house and have a small solar installation that's partially shaded by trees and they drive an EV long distances on a regular basis, then no, they probably aren't going to break even.
We own 3 Teslas, have a large 4 ton heat pump, heat pump water heater (50gal), a pool pump, and an electric induction stove. Our home is fully self sufficient using rooftop solar, and we consistently produce excess energy sold to our utility.
Our utility provides 1:1 metering, so no storage is necessary (and the utility is primarily gas turbine supplied; every clean kWh we provide is some natural gas not burned). We’re self sufficient in the sense that we produce more power than we use. If net metering were to change to be less advantageous, the system was designed to accept one or more Tesla Powerwalls eventually; self consumption would then be prioritized (and I’d shift loads to daylight hours if the batteries were topped up) and drawing from the utility a last resort. Very common configuration in places like Australia, where distributed solar penetration is high and there is an abundance of renewables during daylight hours (causing the spot price of power to go negative much if the day).
In the meantime, it behooves myself and others for battery storage to be installed in places where the grid is far dirtier (remote communities, islands) where storage avoids burning diesel or bunker fuel (versus cleaner but not zero carbon natural gas).
(your comment history looks like you’re pro nuclear/anti renewables, so while I hope my comment was informative, I’m not interested in arguing the merits of net metering, rooftop solar, or nuclear vs renewables).
Sunbelt state. With that said, I have helped install rooftop solar on roofs as far north as Chicago where, when properly insulated, the house can still use a heat pump for heating needs even in the middle of winter (down to -30F) and supports one of the residents commuting 100 miles/day in their Model S. They still have gas backup though.
Keep in mind, the top three states by population are California, Texas, and Florida. Heat pumps can meet the needs of housing in these climates, alongside rooftop solar. Produce where you consume when able.
Edit: I take this back. It depends at least on where you live