Sure, there's "studies" but there's also physics.
My main use of a bike is X miles per day to work and back. Shopping trips and some weekend activities add miles, but the baseline is commuting. I'm not particularly athletic. I have some friends who commute on e-bikes, and I'm fully supportive. It's all good.
Switching to an e-bike won't add hours or miles to my baseline. I mention this anecdote only to illustrate that the effect of an e-bike depends heavily on circumstances.
I think a better generalization might be that an e-bike combined with a lifestyle change can result in better fitness. This is where I see the great benefit of e-bikes, and why I encourage my friends to get them.
Just spitballing a number, if the bike supplies 50% of the effort, then a lifestyle change could consist of increasing your use of a bike by 2x or more. This is not implausible because a lot of people get virtually no exercise at all.
Oddly enough the most frequent question I get about cycling is: "When are you going to get an e-bike?"
I think there will always be a few remaining uses for a bike that is cheap, maintainable by the owner, light enough to carry up a stairs or throw into a car, can be stored anywhere, indefinitely, and used on demand, doesn't catch fire, and is powered by the lipids stored in your body. ;-)