Its usually just an mPCIe card, so no problem removing it if you don't need it.
Yeah, fully integrated is rare, although I could see manufacturers moving that way to cut costs. mPCIe or m.2 cards are far more common in my experience.
As to why you'd want WiFi in a desktop? The majority of PC users aren't enthusiasts who wire every PC they have into their network. It's a simple, cheap add-on that justifies a higher sales price, while a large percentage of buyers see its value. I have a board with integrated WiFi in my HTPC, and while it has a wired network connection (sits 30cm from my modem ...), I use the WiFi card for using a bluetooth keyboard, which saves me the hassle of getting a shitty BT dongle that will inevitably have horrible reception and will probably fail. Also, I've used the WiFi as a bacup internet connection through my phone a couple of times when the god-awful fiber modem my ISP uses has gone haywire.
As for USB WiFi adapters, they have a deservedly bad reputation. They have significantly worse reception than anything with proper antennaes, they run hot, in my experience overheat under load, and are generally a hassle to deal with. Oh, and they usually don't include bluetooth, meaning you need
another USB stick to provide that if you want it.