The short answer is "yes, they do". I have a 19" w/a Sony tube. It has the little wires. Honestly, unless you have your face about 12 inches from the screen (you shouldn't be that close anyway!) the wires are barely noticeably unless you have a white background screen . During regular surfing/gaming/emailing you wont' notice them after about a week of adjusting to a new monitor. Any flatscreen will have these wires. Small price to pay, IMO. It's personal preference though. I've seen many conventional CRT's that have picture quality that rival flatscreens; however, they usually cost more than a flatscreen.
I prefer an "optically correct" picture from corner to corner. I have a Dell E770 17" regular screen that really looks quite nice, but not as nice as my 19" Micron monitor w/the Sony tube. Your mileage may differ.