The filtering reduces crystallization. It also is desirable because most people don't like random bits of wax, bee parts, or really any foreign-looking material in their honey. For better or worse, people like clear, clean-looking honey. The visible particles could be filtered without removing the much smaller pollen, but that'd still leave the crystallization issue. Burleson's has a page explaining filtering, including addressing the claim that it's about hiding the origin of the honey. This NPR article also addresses it pretty well.
Note that some people have made some pretty wild claims about filtered honey not even being honey anymore. This is not true, at least as far as the USDA is concerned:
Filtered. Filtered honey is honey of any type defined in these standards that has been filtered to the extent that all or most of the fine particles, pollen grains, air bubbles, or other materials normally found in suspension, have been removed.
Strained. Strained honey is honey of any type defined in these standards that has been strained to the extent that most of the particles, including comb, propolis, or other defects normally found in honey, have been removed. Grains of pollen, small air bubbles, and very fine particles would not normally be removed.
So if you prefer strained/unfiltered honey for whatever reason, go for it. But filtered honey is still honey.
The heating is better known as pasteurization, and it serves to kill yeast (reducing chances of fermentation) and prevent crystallization/granulation. Pasteurization does kill bacteria too, but bacteria can't generally survive in honey so that's not one of the reasons for it here.
It's pretty easy to find more information about this by searching for honey pasteurization. For example, BeeMaid has a page about pasteurization.
I'm not really sure about the disguising origin theory, given that there are real reasons for this processing that don't sound like a conspiracy theory. I'm sure the processing does disguise the origin, but that doesn't mean that's why they do it. Besides, if you told the whole US that all their honey was from China, I doubt they'd stop buying it.
You also asked about cost difference. That doesn't really have an interesting answer; it's just that raw honey is not as widely sold and tends to be locally produced so it ends up more expensive, while non-raw honey is mass-produced and sold everywhere and ends up cheaper. Sure, it costs more to process than to not process, but mass-production is cheap. This isn't an unusual occurence; white flour is often cheaper than whole wheat, white bread is often cheaper than whole wheat, and so on.