“Then I took a look at the different tools that existed. I didn't like Evolution that much and Mozilla was still in its infancy. Nevertheless, we used it.”
“What's really important is that PGP is integrated directly into the tools. At K-9 I have to install Openkeychain first, at Thunderbird I have to install Enigmail and then GnuPG. Just this step, to have PGP directly, without addon and without additional software installation in the tool, would simplify a lot of things.”
Well, I had PGP “directly” for the past 15 years. It's a matter of choosing the right tool for the job. 😉 I never had to install GnuPG manually (in fact, it's a core package in many distributions: the package managers depend on it since the packages are PGP signed!), and both KMail and Evolution support PGP right out of the box. Mutt as well, by the way. 😉 The lack of a native support is only one reason to avoid Thunderbird and its shaky PGP integration via an addon. There are others that are more basic in nature.
"Which more modern mail clients are there? There aren't that many that are still widespread. It's true that Thunderbird isn't very modern, but there are very, very few really modern mail clients. I don't know of any real alternative."
That's either ill informed or deliberately misleading. It's ok to dislike programs on a subjective basis, but one shouldn't entirely lose an objective stance. Of course there are alternatives to Thunderbird (and with native PGP support), for all operating systems. Windows: eM Client, EverDesk, and of course, The Bat! (the best E-Mail program ever, period). MacOS: Canary Mail. And Linux: KMail, Evolution.
Admittedly, the latter two are not exactly “modern”, although I'm not sure what that is supposed to mean. If “modern” refers to the interface, there's Geary, which was initially released 2012 and has recently become quite popular, having been adopted by the Gnome project and being the default mailer in ElementaryOS. Geary features a modern interface and a modern feature set: it does neither support POP3 nor PGP. Even more modern is Mailspring, the successor of Nylas Mail: it's based on Electron and thus weighs 280 MB, its interface is très chic and themable, and it requires a Customer ID to synchronize mails over the different devices modern people have. It doesn't need to bother with PGP, as there's no need for that in the modern, post-privacy world.
But I'm being sarcastic, and that's not entirely fair, since there are also developments on the other end of the spectrum. The icelandic Mailpile, for example, has privacy as its top priority, and invented an entirely new concept for that: a local webmailer. I would actually consider to use it on my notebook wouldn't the interface be the most dilettantishly designed one I have seen since Geocities.