I don't know about Sweden and the US, but any gaffers I've come across in the UK and Ireland are all qualified electricians. I haven't done a break down, but most DPs I know came through as camera assistants, the ones who came through as gaffers (they start of as electricians in the lighting crew, so it takes a few years to actaully become a gaffer) are the exceptions. There are a few former electricians who now shoot news, but I assume you're talking about another sector of the industry, since they don't have camera assistants in news.
Yeah, the gaffers I've meet in Sweden have also all been "electricians" (Chief Lighting Electrician/Gaffer and Best Boy), however I worked as a "electrician or assistant electrician" and I have no "electrician" qualifications (and thus wouldn't be able to climb the ranks). Basically I hauled lights, and would strike em, gel em, and whatnot. Then it seems somewhat that moving up the ranks in the "gaffing-department" requires lots of qualifications, where as a camera assistant doesn't need to worry about being certified to perform tasks.
The problem I see in camera assistants that wants to become DoP's is that they get to handle lenses, reload magazines, and pull focus, maybe camera operate, but it ends there. I know some that are really good at their job, they get to work on A level films, but they won't get to do any DoP work, not even second unit. I am not trying to belittle any job or any person, but it doesn't seem that weird to me, because most camera assistant stuff seems to just be technical mundane things that doesn't prove your ability as a "cinematographer". There doesn't seem to be much "creative" stuff going on there. Which is the same early on as an electrician, all you do is haul gear. But at the end as a gaffer, you more or less decide or try different approaches to lighting a scene. For me its been when I've done low level gaffing, I talk with the DoP what lights he wants, and I make suggestions for this and that. But when doing camera assistant stuff, I haven't said anything in "try that lens, or we should shoot this on a more open stop, etc". Granted I haven't been on a big budget project as a camera assistant, but I have as an electrician, and what I saw was just a lack of ability for camera assistants to prove them self "worthy" to become DoP's but potential for gaffers to show creative ideas to solve problems.
As I said before, this doesn't mean I think camera assistants are bad or anything. If I am wrong and off, please let me know