I definitely live in Icicle Country and have had the clog-free rain gutters for about ten years, with no unusual icicle formation.
Are your gutters the kind where there is a "roof" over the gutter, that goes past the outer edge of the gutter, then curves back into the gutter? The theory being the water runs down over the top of this little roof, then makes the curve around the outside with surface tension holding the water onto it long enough so that it reverses course (on the underside) and falls into the gutter.
This kind:
https://www.leafguard.com/images/gutter%20guard.pngThat's the way ours are. What happens is that snow builds up on the roof (this time I'm talking about the main roof of the house). As the sun shines and the day warms the snow melts, but it re-freezes to the "roof" on top of the gutter (this "roof" is thin sheet metal and transfers the cold air temperature easily). This causes the outer edge of the little "roof" to grow and grow, extending itself farther out past the gutter, so water flows over that extension, re-freezes, and you have icicles. And if that's not bad enough, during the daytime the icicles melt a little and drip. In our case, in the front yard they drip onto our driveway, in our backyard they drip onto our deck. And that drippy water re-freezes again and you end up with a skating rink underneath the icicles.
Here is a picture of our icicles (you can't really tell it in this picture, but they grow to about 5 or 6 feet long and are wide and heavy at the top - that's a dangerous thing!)