In your metaphor the battery would be akin to the gas tank though, rather than the gasoline that fills the tank. I think my gas tank can be emptied and filled more times than a battery and it doesn't lose capacity the more it's used or when it's cold out!
My metaphor works within the confines of equivalency. Battery aging is essentially equivalent to gasoline engine/transmission mileage, as the electric motors and electronics don't meaningfully age unlike gas engines. You can't run a gas engine forever, as eventually maintenance costs will exceed the value of the engine.
Every gas car I'm aware of loses efficiency when it's colder outside. It's not as drastic as an EV, but it definitely exists. Also, gas engines tend to get slightly less efficient as they age, just as components begin to have higher friction, increased wear, worse tolerances, etc.
