I would have to differ with you on that Bill. I have Solidworks files on the network and when I open one of them if someone else has it open it tells me who has it open. It is built into the software. What can't Adobe build it into its software?
It would be a nice feature and would suggest you follow Bernd's link. However, you asked about what Acrobat can do and it can't, so you have to deal with it on the network level. It is a feature Acrobat would have to add in the system. Then there may be issues about what kind of network are you looking at. Acrobat has had issues with networks over the years and trying to provide information on all of the different types of networks might be an issue. I am not a network user and can only speculate on the various reasons it is not part of Acrobat. Of course, there are things that users have been asking for since AA4 and such that are still not implemented, so don't hold your breath. However, the feature request is the best route for the future -- You will probably not see it in AAX.