At $2000, a Peloton bike is $1000 to $2000
cheaper than the cheapest carbon-frame
bike I could find on Google
Unless of course you're ignoring every sub-$4000 bike as "bad cheap carbon" but that's not what your post says :)
Of course, if you're buying a bike exclusively to use on an turbo trainer, I'm not sure I see the logic to getting a carbon frame anyway - it's not like the weight or bump handling makes any difference.
[1] https://road.cc/content/buyers-guide/254002-13-best-carbon-f...
True, REI has the Synapse on sale for $1700 right now not including delivery. Once you add a trainer of the equivalent functionality as the Peloton trainer, you're looking at $2500 spent. Add in a screen, and you're looking at $2700 for a small screen or $3500 for a similar-size screen as on the Peloton.
I suspect people are overestimating this part of Peloton's market. All the people I know who spin value being a part of the community: the camaraderie of working out with other people, chatting after the class, etc etc. It's more like going to church than going to the cinema.
Peloton addresses two real needs in the exercise marketplace: home-based classes, and high-quality exercise machines. It simply combined both into one product.
There is huge demand for the former, especially from white-collar workers with high demands on their free time, and a a fair amount of demand for the latter.
At $2000, a Peloton bike is $1000 to $2000 cheaper than the cheapest carbon-frame bike I could find on Google, and more than $3000 cheaper than a racing or tri-bike. For indoor use, you'd also need a trainer, adding another $600-$2000 to the cost (depending on the trainer you get).
Generally, the people I know that have carbon fiber frames also have several other bikes, each for a different niche, and the Peloton would slot right into the indoor spin use case.