Yes they should be moderated.
In this day and age, across many forums, people choose to press the quote button to reply to a post rather than editing the post down only to what requires being quoted.
I mean if I wanted to quote Geoff W above, I can press the quote button and do this:
Or I can choose to edit it PRIOR to pressing "Submit Reply" and quote only what is required, ie:
However in most cases it is never generally necessary to quote the person who appears directly above your post when read by others.
Personally, I think the "Reply with Quote" button should be removed and users manually insert anything they believe need to be quoted.
We have a great board and I believe it's professional appearance is something we should all strive to preserve.
Now go on, someone quote this entire post........