Click tracks (or similar) are also helpful in a live setting to synchronize the drummer with looping/sequenced/delay kind of parts to keep them in time. Like, for example, if you have a guitar with a delay set so it “echoes” on every eighth note at exactly 120bpm, it helps to have a drummer with a click playing in his ear so the parts exactly match. (Like, I assume the U2 drummersmust play with a click during the concert, as the Edge’s guitar parts are so heavily dependent on the delay.) Or if you have a synth with an arpeggiator set to a specific tempo. Or triggered rhythmic loops. Etc.
Clicks can make music sound a little stiff, but I don’t think as a rule they do, as there’s still plenty of room within the beats to push and pull. As long as you synch with the one, you’re usually fine.