My Telecaster has frets with a noticeably higher and wider profile than the frets on my strat. Was this the result of someone's personal preference or did Fender have another reason for the choice of fret size?
Mainly down to personal preference, rather like string gauge. Some people's fingers suit a fatter/thinner fretwire, a higher/lower action, tighter/looser strings, wider/narrower fretboard, deeper/shallower neck profile, etc., etc. All these factors and more come together to make the nigh on perfect guitar neck - or not for some - and that's before we get on to body and pups etc.
Just another option which will suit some, but not others.
Higher frets change how you finger notes. To see an extreme example of this take a look at scalloped fret boards. They keep the string from touching the wood and can potentially make you a faster player by playing with only enough strength to fret the note rather than pressing it all the way down into the wood. This is, of course, up to interpretation. Wider frets are more of a consequence of making a fret taller since you want a nice, round cross section to make playing more comfortable. This has the added bonus of making the fret easier to make out by touch alone.
I think the best explanation I've seen for larger frets is that they'll last longer and be more playable as they get worn down from use. If you need a fret level down the line it's nice to have extra material to work with so they aren't filed down too close to the wood.
You will find far more opinions on this than you will find facts.
Standard guitar frets, jumbo frets, c-shape necks, d-shaped necks, and wrap-around bridge tail-pieces; things like this come and go, and what is in vogue this year may be old hat next year.
Here's what really matters: How good and intuitive the frets and the neck feel to YOU the guitar player and owner.
Guitar building is a business. Fads come and go, but making money is at the bottom line of it all. If this fret or that fret doesn't cut the mustard, they will go the way of the Edsel.