Gutters in New Mexico spend most of the year doing nothing, then get asked to move an enormous volume of water in about twenty minutes. That is a completely different design problem from a place with steady, moderate rainfall, and it is why so many houses here have gutters that sheet water over the front edge every single monsoon.
The first suspect is usually not debris. It is size. A standard 5-inch K-style gutter with one downspout is fine for a small roof plane in gentle rain and hopelessly undersized for a large plane during a cloudburst. Bigger roof areas, and anything with two planes draining into one run, generally want 6-inch gutter and more downspouts than a builder installed.
The second is downspout placement. Downspouts often get spaced evenly along the house because it looks tidy, rather than placed where the water volume actually concentrates. A valley dumping into the middle of a run needs a downspout near that point, not thirty feet away at the corner.
Third is pitch. A gutter needs a consistent fall toward the outlet — a little, but consistently. Runs that sag in the middle hold water, and standing water in a gutter is dead weight that pulls the hangers further out of the fascia, which makes the sag worse.
Which brings up the fourth and most expensive problem: the fascia behind the gutter. Water that has been overflowing for years runs down the back of the gutter and into the fascia board. By the time you notice, the wood is soft and the hangers have nothing solid to bite. Hanging a brand-new gutter on rotten fascia is a repair that lasts one season, so the wood has to be replaced first — and that is a roofing job, not a gutter job.
The fix that lasts is boring and specific: replace any soft fascia, roll seamless gutter on site so there are no mid-run joints to split, hang it on hidden hangers screwed into sound wood, pitch it properly, and put the downspouts where the water is. Then run a hose through every run and watch it before calling it finished.