Low power cycling (and powering a house is miniscule draw for a car) below 80% SOC cannot induce enough wear on a car battery to show up at all before calendar aging makes the battery unusable (which is about 10 years after the rest of the car has worn out on average). And the range it reduces is about 10% for an evening of powering a house, leaving more range than the typical ICE has when it is parked with the tank less than half full.

As to the investment. A tesla 3 is $40k and has an 86kWh battery in it (82kWh usable). Modern LFP batteries are rated for 8000 cycles at 0.1C (8kW or about what you can squeeze through a reasonable-sized wire at 240V ). If you somehow manage to wear it out and got 8c/kWh, you've made a profit. At 30c/kWh spread that some people pay, that's tripling your investment.

You can only 50% drain your battery during peak 5-9pm consumption though so this will take 22 years of going full-tilt every day. The other 1.5 cars in each average household won't get a turn, nor will several of your neighbors because peak electricity consumption is under 8kW per capita pretty much everywhere.

If you are lucky enough to wear out your battery this way, it will pay somewhere between 50% and 300% of the TCO of your car depending on where you live. 5% isn't a great investment, but it also comes with a free car (and currently up to $8k ofnsubsidies not counted above).

Powering a couple appliances for a few hours is nothing for a car battery, those things are huge and powerful because cars are so inefficient. That's not to say that V2G or V2X will work perfectly for everybody, but with the average commute around 25 miles and plenty of EVs out there over 200 mile range (which equates to mutliple days of typical electrical usage), there's certainly some extra capacity. If you were compensated for the power you sold back at peak times, it could help justify paying for and lugging around the kind of battery capacity that is specced for your weekend/holiday road trips just to make your likely shorter daily commute. I'm using you generically, I don't know your specific situation, so you certainly could be someone who would not feel a need to engage in that kind of scheme

It is a very solvable problem, and mechanical or thermal batteries are likely to be at least part of the solution. Of the three kinds of gaps/shortfalls that grid storage would have to cover, the milliseconds-long and hours-long gaps are probably the easiest to solve. The days-long gaps (stretches of cloudy days, low winds for extended periods) is probably the most expensive to solve, but even those are not really that difficult (hydro storage is a tested technology that works well and HVDC transmission linking regions together can allow local shortfalls to be covered by remote surpluses). It's all more a matter of building capacity than needing new technology to solve an unsolvable problem, from what I understand

Longevity is the big problem. Every practical method of energy storage I can think of is negatively impacted by frequent charge discharge cycles. Even a flywheel like you suggest would eventually need new bearings, need rebalancing, etc....

You don't need a lake, just a hill or a hole. And the only places without a vast excess of pumped hydro resources have amazing solar and wind resource so don't need it.

A renewable system with PHES for storage is both viable pretty much everywhere, and significantly cheaper than thermal generation. They likely won't get built because it's not really competitive vs batteries for short duration storage, takes a lot of time/coordination, and storage requirements are about an order of magnitude less than the fossil fuel shills are claiming.