You don't need to run it in browser at all, there are desktop (and phone) clients for every major OS out there. This shows that you are really not familiar with it.
Now it is still a crappy system, but for different reasons than you describe. And other solutions have their own problems, as indicated by article and elsewhere.
My university uses it as well, and the normal latest version of Webex is on par with Zoom. However for some courses the lecutrers use e.g. Webex Training which is barely usable garbage (but is the only version that has built-in quiz features).
I don't care about anyone else's OS. I have desktop zoom, desktop slack, and desktop MS Teams, all work fine. Webex has web only (which means no whiteboard -- which I'm told from people who do have supported desktops -- mac users I think -- isn't good), no joining of private rooms, and the awful spyyware ability of remote people to turn on your microphone without your permission.
Now you sound as if you are not familiar with it. Looks like Webex added Linux(Deb & RHEL) on May 28, 2021. Before that, you had to use their legacy java applcation which also necessitated you to *manually* figure out, then hunt down & install the missing dependencies. And it was still shit.
Webex - which I have to use as part of a university course I'm doing on the side - requires you to run it in a browser on my OS, it has really awful options (like allowing the presenter to unmute people), half the claimed features just aren't available (virtual whiteboard, no major loss as everyone uses a shared google doc instead), and if you disconnect for some reason (like sound stops working which happens fairly frequently) you are kicked out of a group and you can't get back in.