Using ones shiny Tesla as a battery bank is only sensible if your wallet is deep and you shut your eyes when you watch how fast it's emptying. Such a cars lithium battery at say £10K new lasts 1000 full charge cycles. Every time the leccy company borrow some of your stored capacity you may get paid a profit on the energy cost down the cable but does it cover battery degradation?
You are very wise to be sceptical but the battery situation is better than you describe.
The more durable type of storage battery for solar PV is lithium iron phosphate. These don't have the highest energy density like you need in your electric car, but they do last better. The major brands all guarantee their battery packs for either 6,000 or 10,000 full cycles, at the end of which they still have 80% of the initial capacity.
Using rough numbers, £10k will cover the cost of the electronics and 16kWh battery in my own planned solar install. Battery is guaranteed for 10,000 cycles, and over the guarantee, will drop from 16kWh to about 13kWh capacity. Average about 14.5kWh.
So £10k / 10,000 cycles is £1 for every 14.5kWh I put through it. Or 7p / unit to store my "free" (not really of course) solar power to use when it's needed.
In practice, I expect a few years for free after the 10yr warranty period because I won't bother replacing they cells until they are down to (say) 65% capacity.
Now the feed in tarrif is gone and the export guarantee pays only 5 to 6p per unit, there is no benefit to me letting the grid draw on my planned battery storage. They pay less than it cost me. The key to modern residential solar is: you make it, you use it.
BTW, lead acid isn't a good technology for any of this. China is full of electric scooters powered by 4,5 or 6 lead acid batteries. They are cheap and great fun, but the batteries are worn out after a couple of years commuting to work. Those really don't achieve 1,000 cycles, and by the end have nowhere near 80% capacity left.
There are other wet cell batteries with far longer than 10 year lives but bulky and not lead acid tech.