The first herd of goats we bought were polled. Breeders told us the horns get caught in fences and cause a lot of problems. They weren't wrong. The second herd we purchased were primarily horned and some got their heads caught in all sorts of things. Having tried both, we prefer horned goats.
The last few polled goats are set for our August cull. We plan to keep some of their kids, but move the hornless goats off to some other farm. Cull might not be the right choice of words. One doe is really nice, but she is also aging. But she is a handful to work.
We use the horns to control the goats during worming, vaccinations, or checking the color of their eye lids. Without horns you end up grabbing the ears; these are a lot harder to grasp. It also means you get to re-tag them when the ear tag rips out. Yep, now the doe is really hard to handle because her ear hurts, not to mention that blood on your fingers is just a little slippery till it starts to dry. No - we like the horns.
Horns offer some natural protection. Some breeders disagree and suggest goats really tend to flee rather than fight. This is true to an extent, goats aren't notorious for fighting predators. But we still remember No. 11 ( she died last fall after a long productive life ). She could run off most of our Anatolians when she wanted. Granted they knew their job was to protect her, but she taught many a year old pup to keep their distance from her and her kids.
Last, if you run horned and polled goats, we promise you the goats without the horns suffer a disability. When heads butt, the lack of horns leaves one goat disadvantaged. At the end of the day, it is a preference every farm determine for itself.