I believe that the troops should follow the guidance provided by BSA. There is no age requirement for attaining Eagle other than the built in one of serving in an job of responsibility for a specific period of time.
I've sat on Eagle boards and understand that each scout can be very different. I've been impressed with the well-spoken 14 y/o scout who knew what he wanted to do vs the 18 y/o who just barely made it under the wire and didn't have specific plans for his future despite being a senior in high school. I think that artificially holding scouts back from making their ranks despite having met the requirements is not only frustrating for them but contradictory as many troops have the goal to get the new scout through the First Class Rank in the first year. So they make First Class, then what? How would you like it if your boss said you wouldn't be getting any raises until you reach a certain age?
Attaining the Eagle Rank although highly commendable is not the end of scouting. So many scouts drop out at that time because they have reached 18 y/o. We are trying to show the scouts in our troop that this can be a life-long activity. Higher ranking scouts are encouraged to become staff at camporees (they love doing this); earning Eagle Palms are discussed with scouts as the next step; Eagle scouts under 18 y/o become JASMs and teach skills while those reaching 18 y/o become Assistant Scoutmasters.
I've been involved in various troops over the years and know that troops can be as different as the scouts within them. I've transfered out of troops that were not boy-led and those that had their own ideas about Eagle qualifications. You may have to consider this option.
A Scoutmaster can give a scoutmaster conference at any time, not just for rank advancement. In fact, it is encouraged to give one to those scouts not advancing to encourage them to do so. I agree with Gold Winger that the scout should ask the SM, point blank for a SM conference for Eagle. If the SM refuses, ask for the reasons in writing. Take that to the District Advancement Chair (at this point the parents should get involved). Often the Unit Commissioner can help to mediate within the troop. If not, the district may have to. I've seen where an SM refused to give a scoutmaster conference for Eagle (whether or not the scout would pass was immaterial). District was asked to intervene. SM was steadfast so district arranged for the SM conference and the Eagle Board of Review. The scout earned his Eagle rank without reservations by the SMs involved or the Eagle Board. The scout involved is now an adult and still highly involved in scouting and well on his way to a lifetime experience in scouting.
Good luck with your efforts. Remember that scouting is about the journey and we often learn more from the problems that arise than if everything went smoothly. Use this as a learning opportunity for your scout.