I'm not much for a guitar player but for whatever reason I'm drawn to Telecasters myself. I prefer Precisions as well so I guess its just the simplicity and the fact of if it aint broke dont fix it. Very rarely if ever does someone get it right the first time but Leo Fender sure did. If I didn't already have a Tele I for sure would've bought the Hot Rod Tele before my jazz. I'm still keeping my eye on the Hot Rod Strat.
I know you said about the strat but that California Blue Tele with the Rosewood might be more your style.
Already got the Dolphin Tele so that is why I’m looking at Strats. Excuse the bad photo