Is there any reason not to install a bathroom fan roof cap very near
the edge of the roof, about 1.5 feet from the rain gutter? There is
no soffit on this side of the house. Because of the location of the
bathroom fan, the closest, most direct venting would be if the roof
cap was near the edge of the gutter. I have a ranch style house, with
gutter all the way around if that helps.

This is at the rear of the house, so aesthetics isn't an issue.