Drummer, and I know the click is divisive. My take: it’s not there to make you robotic, it’s there to show you exactly where you rush and drag so you can choose your time instead of leaking it. Where does everyone land - and how do you practise with it without playing stiff?
Rhythm-section vote: yes. The trick against stiffness is to set the click on 2 and 4 (or just beat 1) instead of every beat - you keep the reference but you’re still responsible for the groove between the clicks.
Same in jazz - practise phrases against a click on beats 2 and 4 and your time feel transforms. Click on every beat is training wheels; widen it as soon as you can.