I love Goosberry Mesa and go a couple times a year. I would hate to see it closed and don't think that is the answer.
To say that there is not an environmental impact is wrong though. It used to be you would only see mostly "hardcore" (I can't think of a better word) riders. The single track sections were single track and not the wide roads they are now. Now I see people on department store bikes and rentals. Not that anything is wrong with that, we all were there at one point, but there seems to be a different mentality towards maintaining single track and general environmental awareness and "leave no trace" practices from some people that go there now; ie. ghost trails, garbage, cutting trees, TP etc.The desert is a sensitive area to that type of use. The mainstream masses have discovered this place and have started to have an effect on the area much like Moab is in some ways.
It seems like the BLM is taking steps to help the situation with the toilets and the signage in the area. I am sure there are local clubs in the area that also do a lot to clean up and patrol the area to stop ghost trails also. Instead of telling the BLM to "shove it" which will only make them want to close it more, try working with them to keep it open. Contact the local bike shop in the area to see what they recommend to do.
The BLM in that area seems to want to encourage riding. It they let the Red Bull Rampage run in that same area they are definitely for bikes in Hurricane area. Is that the area they are closing? Riding straight down the sides of cliffs and gullies,building unsustainable trails and jumps like that are more likely to make the "tree huggers" upset. I wonder if that is what might be closed down.
"Welcome to Obama-nation"
"While I too would like to see some verification on this, unfortunately this does not seem out of the realm of possibility in the near future considering the current political climate."
(I can't figure out how to do quotes)
Usually it seems to me that the BLM is more like the Bureau of Livestock and Mining and the environment is lower in the equation. The current administration would more likely close this area down if there was a chance of any kind of drilling available. Its happening in Moab now with trails. I don't believe that an Obama administration is going to close access to areas like this, but maybe they will limit the drilling in sensitive areas around national parks that are affecting trails in Moab.
http://www.tetongravity.com/forums/showthread.php?t=140005
http://www.utahmountainbiking.com/UMBphpBB2/viewtopic.php?t=5237
Just my thoughts on the subject.