I don't see where in the AIM to make a full call on initial call up for airborne, only request for FF while on the ground. For airborne, it gives one example "Miami Center, Baron Five Six Three Hotel, request VFR traffic advisories." Then it gives another version if radio reception is reasonably assured but still doesn't give everything needed for FF "Atlanta Center, Duke Four One Romeo, request VFR traffic advisories, Twenty Northwest Rome, seven thousand five hundred, over."
Having talked to Atlanta Center on several occasions, I can tell you the odds of the controller getting everything on the second method, is slim. Perfect example of why full calls don't work most of the time was my flight out to FQD for lunch earlier this year. I'm cruising along with FF with Atlanta Center and a female student pilot flying a Skylane calls for FF with a full call up. As she's doing it, I'm saying to myself, he's not getting any of this, maybe your callsign. Sure enough, he calls her back with "Ok, I heard a Skylane calling for flight following, say again your callsign and request." Long transmission completely wasted because the controller was either busy on a landline or her call was blocked / talked over by someone else. Not more than 2 minutes after that, another perfect example occurred of why a full call doesn't work, but this was due to poor radio reception. A flight of 2 military aircraft called looking to pick up FF but their radios were scratchy. Sure enough, "Ok, calling with a call sign of one one, your radios are broken and unreadable say again."
Personally I don't get burned up with people using full call ups on initial. I've just heard too many times where the controller doesn't get all, or in some cases, any of the information and the transmission just clogs the frequency. Are there controllers that can be on a landline, listen to an aircraft on the speaker, write on a strip while still talking to the other controller? Yep, but they're rare...especially these days.