The current policy (again, this is a separate document from the rule that is currently out for comment) for E-LSA does limit operators to one per FSDO area, and they are only eligible if they have been providing training since 2010. This was done to grandfather a few existing E-LSAs despite the fact that the rule didn't allow them to provide training. Other LODAs, such as E-AB transition training authorizations, have no such restrictions.
The NPRM changes the rule to make training in E-LSAs legal again, and the policy revision (at least if it is published as drafted) will allow ALL experimentals with a Vh of <87kts to be used in primary sport pilot training, with no geographic or duration restrictions. The FSDO will still have some discretion, but in our experience the vast majority of qualified LODA candidates are successful in applying.
So if you're basing your understanding of the process off the current policy, found here: http://fsims.faa.gov/wdocs/8900.1/v0...03_011_001.htm, just know that the policy should be changing to something significantly different soon.