Good observation! It was like that until very recently. When I first became a mod, getting a trophy was tied to moderation powers so the "Award Trophy" button was always there but I never clicked it. Later on when Alex came back and EndMaster got a trophy, Alex separated mod powers from trophy-giving in the site code.
As far as I'm aware, Solo, Havvy and Paul can still award their trophies despite no longer being mods (though they're no longer active anyway).