This is a question that's been on my mind. I've only ever beaten Ithaqua with a single investigator, I've beaten Pharoah with both a single and with a team of two or three (never four), and I just recently completed a little personal challenge of beating Yig with every Investigator in a row (but not in one sitting) without ever losing a single game.
I know one of the big draws of multiple investigators is that not everything is riding on one character, that if one person dies its no big deal. Plus, you get a variety of abilities to draw from. But I think the benefit of loading a single investigator up with trophies and items outweighs any potential negatives.
It also seems a bit more thematic, as Lovecraftian stories usually center on a single character going it alone as their world closes in around themselves. So, let me slightly reword the question in the topic line: Is there any campaign/ancient one that you can't solo?
Also, nothing to do with the question above, but I didn't want to start a new thread... does anyone know how exactly Jim Culver's ability works? It's never made sense to me!