I'm aware that there have already been posts from people about F-Droid, but none of those I've seen address this particular proposal.
Instead of publishing the apps on an F-Droid repo hosted by Izzy or F-Droid, you could simply make your own. This is common practice among companies that have a privacy/data protection focused user base, just as Kagi does. A few examples are Bitwarden, Brave, Session, and Futo. Hosting your own F-Droid repository would mean you're in full control of how to distribute your apps and which features they contain, and it would also allow Kagi users to obtain and use your apps without using Google services, which are well known for not taking consumer safety seriously and are, ironically, one of your direct competitors in the market.
You may argue that it is possible to obtain apps from the Google Play Store through the third-party Aurora Store, and while this is true, time has shown that Aurora Store regularly deals with technical issues, be it rate limiting or others. It also violates Google's legal agreements and is less secure than the actual Play Store, according to GrapheneOS.
Making your apps more accessible by distributing them through your own F-Droid repository would further prove your commitment to user interests and privacy, and also make it more appealing to potential users. I've been subscribed to Kagi for over a year now, and while I'm not pleased with all the decisions you make and the fact you're a US-based company, I still really like many of your services. I hope I did not invest my money in a company that only pretends to care about user's interests but actually acts on it.
Learn more: https://f-droid.org/en/docs/Setup_an_F-Droid_App_Repo/
