The point of restricting specializations isn't necessarily to challenge the universality of bonuses. There are certain skills that already start with a high level of blanket usefulness. Pilot Ground Craft is one of these, since having a few points and a specialization in (Wheeled) makes you equally good at driving your minivan, a dirt bike, and an F-1 racer.
The First Aid (Combat Wounds) example isn't egregious, but it is still pretty broad. First Aid (Gunshot Wounds) or First Aid (Blunt-force Trauma) would probably be better. Generally, First Aid (Source of Damage).
Personally with First Aid, I don't know why they split it from Medicine in the first place. I'd prefer the old Biotech (First Aid), really.
As for Pistols (Ares Predator), it gives a high incentive to keep using the same gun, sure. And certainly the character will use it for every pistols shot he can. But suppose the character with the Predator specialization loses his gun somehow, to a spell or explosive, or he gets stunned and drops it in the river. One of his assailants has a Colt Manhunter on him, which will get him by in a pinch but just isn't the same.