Depending on the UV settings, it will kill pretty much everything that goes through it, meaning all the free floating critters in the water column. A lot of this stuff is a food source for your filter feeders, so that's not a good thing for them. Also, many beneficial critters spawn via clouds of sperm/eggs--going through the UV kills them, which isn't necessarily bad, but it means you don't get self sustaining or spreading populations.
UV set low enough not to kill larger organisms is not going to efficiently kill the smaller ones, which means the UV isn't even doing the job you wanted.
I know several people who had serious nitrate problems after installing a UV to run full time. Turning off the UV brought down the nitrates.
I do think that a UV is useful in a quarantine tank, just not for a show tank (for SW and FW). Ask yourself why you're running the UV--because UV doesn't do anything to improve quality of water. All it doesn is kill things--some good, some bad. Since parasites are best dealt with in quarantine, and most other "UV-treatable" problems can be better and more easily treated with other methods, they just aren't needed IMO.
For skimmers--yep, they do remove some of the good dissolutes along with the excess protien. However, a skimmer really does remove them, and the iodine, etc can be easily replaced with regular water changes.