There's an interesting blog post about this topic: https://keith.seas.harvard.edu/blog/climate-impacts-biking-v...

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.

According to this article, ebikes do produce fewer carbon emissions than conventional bikes overall, while considering manufacturing costs:

https://www.bikeradar.com/features/long-reads/cycling-enviro...

Judging by people's waistlines they're already eating the extra needed for the cycling, they're just not cycling.

According to COVID-19 and Obesity: The 2021 Atlas[1], the figures for the UK are:

- 63.7% of adults are overweight i.e. BMI >25kg/m2 (2016)

- 27.8% of adults are obese i.e. BMI >30kg/m2 (2016)

[1] https://www.worldobesity.org/resources/resource-library/covi...

Obese people won't get on a bike, though, because it's too big of a step. An ebike is a decent gateway into weight loss.

Exercise is for health, diet is for weight loss. The overlap exists but is minimal. Exercise activity hermogenesis (often known as EAT, ironically) is usually estimated to be around 5% of total daily energy expenditure (TDEE).

I wouldn't be surprised if the obese people in question started to exercise and actually increased their food intake to match.

That's assuming you'd just eat less, instead of eating the same and burning it off at the gym. Or getting fat.