Well, whose fault is that?!?
Very similar to other recent vintage Tele's I've played. Not real thick, not real thin. I find them very comfortable to play, but then again I've noticed that I seem to be pretty non-discriminating when it comes to neck thickness vs. many other players. The current specs on the Fender website say it's a U-profile with a 7.25" radius, but this one really doesn't look or feel that round to me--more like 9.5" and it feels like a C profile to me. So maybe the neck has changed over the years, since this is a 12 year-old guitar.