That assumes the battery behaves the same for low and high current (they don't). Even lithium cells already don't; high currents causes them to warm up, reduci

That assumes the battery behaves the same for low and high current (they don't). Even lithium cells already don't; high currents causes them to warm up, reducing capacity. So a device that draws 1 Watt will last longer than one that draws 10 Watts from a small lithium cell. Lead Acid responds even worse, especially starter batteries, less so on deep cycle, and it's capacity rapidly changes, without temperature influence. A 1 Watt device might only last a day while it's fine starting up an engine with 10 times the total power consumption