I understand the concern, but anyone wanting details of where the various stone axe quarries are only needs to go onto the Archaeology Data Service homepage, or trawl the internet. Anyone determined to search for an axe roughout, or any other souvenir at any other site, will do so, regardless of whether it features on TMA.
I think TMA provides a good source of information on what to expect at a site, and it'd be a shame to lose that due to fear of what people may do once there.
Cheers,
TE.