I worked ED -> Derm/Mohs -> Ortho/Hand -> Neurogenetics/Complex Disorders -> Interventional Cards/Nuclear -> Family before applying to medical school.
I can tell you, categorically, that the FM environment is significantly different from any of the ultra-high specificity specialties I'd worked. I would think it's important because I noticed that in FM, you spend an extraordinary amount of time with the patient; like 45-minute visits. That's insane. In Derm or Hand, we could see up to 70 patients a day by overbooking 15-minute slots. The kind of interaction you have to have in order to fill that time in FM is significant, and I think the physician actually works harder because there is economic and administrative pressure to make the time you have in the room with the patient be productive.
It is also alarmingly versatile: where in Cards, for example, you're coming to execute a stress test and nothing else, in FM, you could have 5 totally different pathologies across different body systems you're expecting to resolve in one visit. It's a lot of documentation, variety, and communication with the patient that often results in long, diverse treatment plans that require professional coordination and sometimes upwards of 5 different referrals. Then there's medications and other treatments; patient education; and the unspoken but universal expectation that the physician be a vigilant monitor of all of these... they really deserve to be paid more, but that's for another time.
Logically, the specialty hierarchy is a pyramid, from high-scope specialties like primary care, up to the most niche sub-specialties. While all specialties are technically practicing medicine, it would make sense from the medical school's perspective to expect that applicants have experiences with the full breadth of medical practice...which is only available through engaging with the most generalist specialty available, often FM/IM in a primary/preventive care setting. It's the specialty everyone thinks about when you say "I need to go to the doctor."