Your theory is worth discussing.

While in an absolute instant sense energy use might win for the machine, you probably forgot to factor in the lifetime cost of the production of the machine's components. I do not blame you as such a task seems exhaustively daunting, and we only ignore it for the people because who would be heartless enough to think that way? (probably insurance agents, lawyers, and such...)

There are also pros and cons to the different elements. Exercise on a bike might have a hard to measure benefit compared to an e-bike. On the other hand adoption pressures and increased hygiene needs are more positive and negative side effects.