There is a pending flathub submission request for itch.io that's waiting for feedback from the itch.io developers before it can be submitted:
https://github.com/flathub/flathub/pull/3719
Having itch.io on flathub would make supporting Linux easier due to providing an installation method for running the client across all desktop Linux distributions. I can confirm that the client in its current form works well as a flatpak, being able to run native Linux titles as well as run Windows titles with Wine.
The Steam client for example has 1.1 million downloads (unique, not including updates) at the time of this writing:
https://beta.flathub.org/apps/details/com.valvesoftware.Steam
Installing Steam as a flatpak is currently one of the most popular methods according to the Steam hardware survey:
https://store.steampowered.com/hwsurvey?platform=linux
I hope that the Linux ecosystem can converge on a standardized application distribution method for supporting all desktop distributions, and flatpak appears to be one of the best technologies to achieve this due to the level of runtime isolation that it provides to ensure a consistent experience and the simplicity it offers with one-click installs. The Steam Deck already uses flathub for simplified installation of third-party applications: