It's a nice idea but it wouldn't work. The gasoline would go bad before you could use it all.
Plug-in hybrids already have this problem. Their fuel management systems try to keep the average age of the fuel in the tank under 1 year. The Chevy Volt has a fuel maintenance mode that runs every 6 weeks:
https://www.nytimes.com/2014/05/11/automobiles/owners-who-ar...
https://www.autoblog.com/2011/03/18/chevy-volts-sealed-gas-t...
Instead of having a "lifetime tank", a car that uses 0.005L per 100km would be better off with a tiny tank. And then instead of buying fuel at a fuel station you'd buy it in a bottle at the supermarket along with your orange juice.