I'd be all over the CV Tele if it weren't for the thin neck. I already have a strat that get little play because it has a modern thin 'C' profile. It's a shame they don't offer an alternative 'regular' neck option.
Yeah, that's one thing missing from the Fender range - they should offer a choice of neck shapes, at least for the basic, meat-and-potatoes models like the American Standards. Maybe a "C" and a "soft V".
There
are lots of different shapes, but only if you get a completely different (and often more expensive) model. That was one of the reasons I got the Robert Cray Strat, for the big round neck.
Having said that, I'm reasonably comfortable with the current "modern C" shape - I'm just glad it isn't any thinner.