I am a former state government employee who is actively seeking a federal employment. As such, my responses are going to be inspired by my day to day experience and observations:
I believe there are a few things the federal government can do better in order to recruit the best and the brightest, regardless of where those candidates are. Here are some of my thoughts on the matter:
1. Allow current/former state employees to identify themselves as such, during the federal job application process. Often, the same duties, etc, are highly transferable, save for the pesky little boxes a state employee cannot check/ or an outstanding ranking form letter that a state employee cannot submit 🙂
2. Allow for an equitable 'time in service' once employed. Perhaps a 'one to one' transfer may not be equitable, much like one cannot transfer all credits from a two year college to a four year university -- but a baseline should be able to be arrived to. Much like credits are given to someone who is applying higher education to a position's band, perhaps a similar system can be worked out for a local government employee.
3. Inject a clearer job requirements description into the actual listing -- often, the federal jobs are cut for a one size fits all in all aspects, and most folks do have a specialty in one of the many areas the federal listing is mentioning. In the civilian world, this would be known as 'xyz skills/experience' a plus, etc.
I am certain there are many others, but those three are the single most important aspects of ensuring one can take advantage of the quality and experience that is often reflected at the local government level.