With incognito mode data is still fetched client-side: the browser still has to send requests directly to the target platform. Plus the origin platform will still set session cookies.
Instead PR (and as far as I know all other alt-frontends) fetches data and does scraping server-side, so that the browser never contacts the platform directly.
The idea is that you can host these alt-frontends wherever you wants (eg. on a remote VPS) outside of your network and they deal with the platforms as intermediaries, and people just have to open the proxy website and browse for content...
Fingerprinting from the original website is easy, the frontend will have a fingerprint as well but it should be shared by all the users without exposing their browsers. Better privacy therefore.