There was a recent question about exercise bikes.
Do we consider these on topic or not? They don't really share much with a conventional bicycle.
There is a tag stationary-bike: only seven questions so far, but some of them have thousands of views. The question you linked to is missing this tag, and possibly there are more exercise-bike questions that are not tagged correctly.
Most of such questions have been well received. After all, it's the audience that counts most, not the technical characteristics of the device. And the audiences overlap. Sure, real bicycling is very different and a lot more fun, but where I live, doing it outside in winter is a serious adventure...
My suggestion: add a synonym [exercise-bike] for [stationary-bike], to increase the tagging accuracy. Those who are really not interested in anything stationary can ignore the tag.
I vote: yes.
There's a spectrum of "ride bike without moving" options, from rollers that a regular bike rides in place on, to trainers that a regular bike is bolted into, to dedicated bicycle-style exercise machines that have a lot in common with bicycles, to dedicated bicycle-style exercise machines that don't have much in common with actual bicycles.
If an exercise bike has standard bicycle pedals, a normal bicycle chain, can mount a regular bicycle seat, etc, then this is definitely the place to ask.
I don't think we can reasonably try to draw some line in the middle of the exercise bike spectrum and expect anybody to understand it.
Probably don't want to allow exercise devices that don't have pedals that you move in a circle or otherwise just don't resemble a bike (ellipticals, treadmills, etc etc)