My primary tele is a 62 reissue. The neck and body are great, but I didn't like the original pickups, so I replaced them with Lollars (still single / single config). Also I replaced the bridge plate with a Joe Barden brass plate. While I was at it, I swapped out the stock switch for a 4-way version, so I have the three standard tele modes (brige / both / neck), plus the fourth position : both pickups in series, which gives you a huge fat jazzy tone. Also, if you have a tele with a six-saddle bridge, I'd strong suggest swapping it out for a compensated three-brass-saddle version. In my opinion, for a great tele tone, you want as much positive string-hardware-body resonance as possible. The combined downward pressure of two strings on a shared saddle sounds much better, as does stringing through the body.
I knew the neck / body combo on this guitar was great when I first played it, but I also knew it was being hamstrung by the crummy pickups and the stamped bridge plate + stamped saddles. Once those mechanics were addressed, my inexpensive tele really opened up.
A tele is a super honest guitar that reveals playing nuance. You *can* just thrash on it and it'll make guitar sounds, but it will also respond to great technique and dynamics. I've always been impressed with tele players who can sound great when plugged straight into a Fender amp with no effects.