yeah the idea of the click-to-respawn mechanism is actually to protect idle/distracted players from beeing killed all the time (or from the other side: to minimize the free kills for other players).
so you really should add an automatic "afk"/"idle" detection if you want to remove the click-to-respawn thing.
I don't think that this single click is annoying in any way. people are familiar with it because nearly every shooter with respawning does it that way and you click all the time anyway.