From a procedure design viewpoint, the minimum altitude at the FAP is just that - a minimum. About the only reason I can think of to justify the descent might be to avoid a false GP. However, if you start down from 3,000 feet at GP intercept and pass the FAP at or about 2100 feet, it'd be a fair bet that you're on the correct GP.
There may be some local condition or other that makes it advisable to descend to 2100 feet after passing the FAP but there would probably be some sort of explanation about that on the chart, or in related documents for the airport. One of these might be related to short range on the GP, but this would surely be notified in an official publication.
However, all things considered, I see no operational reason not to intercept the GP at 3,000 feet - if you can independently confirm that you're at the right distance from the landing THR.