tl/dr:
They’re an old spec from 2002
They’re too small to click for people with increased accessibility needs
They serve the needs of app publishers (making their app visible at all times), not those of the user
-> There are too many of them
-> They look bad
i cant think of any valid reason gnome doesnt have official system tray icons
Gnome’s official stance on that matter:
https://blogs.gnome.org/aday/2017/08/31/status-icons-and-gnome/
tl/dr:
They’re an old spec from 2002
They’re too small to click for people with increased accessibility needs
They serve the needs of app publishers (making their app visible at all times), not those of the user
-> There are too many of them
-> They look bad