I've both soft and hard modded Wii's of varying age. They sure get louder with a DVD-R, DVD-RW, or Dual Layer game, but clicking? Modern non-tray drives make a click noise when you put a disc in, ever hear a Macbook make munching noises when you put in a disc?
You make a very good hypothesis bazamuffin. However I don't think it's normal for the drive to be "clicking" while playing games and the only ones I've heard do that have been developing disc read errors. The OP also does not say that he has this problem with every Wii hes's encountered but we do have a lack of information here. Soft/hard modded?
If you guys are all adamant that your Wiis make "clicking" noises while playing games from a DVD+/-R I'll back off, but I have never seen this from my friends' healthy Wiis.