Let's say in my case, that's 5 kWh usage between getting home from work to going to work next morning. This assumes the worst case of zero grid power after I get home from work. Out of 60 kWh battery, that'd be only 17%. Maybe you need to define what would be considered deep cycling first.
Go to: California ISO - Supply
Scroll down to the chart on Storage. This is how much the batteries are cycled currently in California.
If everyone drove EVs, that just means much more solar fields can come online so people can charge their EVs during daylight hours then driving their EV home to provide bulk of the power to the house during the huge evening peak and also the next morning's smaller peak. Over night, can probably do a little recharging from wind.
It's not just *your* house, you are thinking too locally. See my post here: What happens if everyone drove EV?.