I absolutely would, in fact it's a major reason I am not getting a Tesla and am instead opting for an EV that emphasizes its vehicle-to-home power capabilities (e.g. F150 Lightning and Lucid). I also know a ton of other Texans who feel the same way I do given our (deserved) lack of faith in our electric grid.
Also, saying it's "feeding power back to the grid", while technically accurate, isn't necessarily how I think this will be messaged. Instead, I think it will be messaged that, in times of high demand, your house alone will be powered by your car battery and taken "off grid".
Right now, some of the biggest issues with renewables is just timing during the day (e.g. late afternoon/early evening power needs peak right as the sun is setting). Telling people they'll get a substantially discounted rate if they allow their house to be "disconnected" from the grid for a few hours (because they have a car battery that can power their house) would be a big incentive to a lot of people.
And yes, V2H power can increase wear on the battery, but my understanding is that large strides have been made (and certainly will be made) in reducing the wear impact on the battery.
A few kWh from the middle of the charge range has about zero cost to battery life, and the owner has to pay the carrying costs of a car anyway, so their costs will be less than the cost of dedicated grid storage for those few kWh.
Not sure if you're just talking about something specific to your house, or making a broader point.
Once EVs are widespread, they can add a huge amount of storage capacity to the grid. Not hard to imagine utility and government incentives that encourage car owners to make some of their battery power available at peak load times.