Do you list journals you have reviewed for on your CV?
On the one hand, it shows that you are engaged in this necessary part
  of scientific research that is peer-review.


That's one of the major reasons why people list it. If your CV is being viewed as part of a performance review or hiring decision, or even for awards, this constitutes "service to the community" and indicates that you're a good citizen.

It's a noisy signal for the reasons you indicate, and so it doesn't carry a whole lot of weight compared to things like technical committee memberships and leadership roles, but it's part of the larger picture. Moreover, for more junior researchers who haven't yet had the chance to take on leadership roles, this is a good signal of service.