Good start, but you haven’t factored in the multiplicative % losses from converting the stored electricity from the battery back into locomotion.
This is the bike you only have to pedal 5 km, to travel 3.
I left out a discussion on the mechanical-electrical-mechanical conversion losses because I wanted to focus on just the chain itself. My argument being: if a chain can do 97%, how on earth will a chainless system do better? Answer: it can’t, not for the commonplace bike or ebike.
But you’re absolutely right that the double conversion loss must be horrific. Even EVs have contended with a similar choice before and today’s hybrids do tend to be parallel hybrids.
Locomotives are, I think, the only widespread application where the benefits outweigh the costs, bevause the cost of a behemoth transmission for a diesel locomotive would be prohibitive to build. Hence, diesel electric locomotives.