Is it someone who can hammer for 45 yards in gale-force diagonal winds? Is it someone who can casually flick huck from the back of the endzone for a score? Is it someone who can break at will, and throw an around-the-back? Is it someone who can fake a low flick into a IO chicken-wing from brick to goal?
Probably not.
In the context of a beginning, new, or intermediate team, it probably means none of those things. Your best handlers are the throwers who protect the disc. It might not be who you think it is. It might be the guy who will only throw 10-yard throws on a backhand but converts EVERY SINGLE TIME. It might be the gal who always take 6 counts and only has a mid flick and dumps 60% of the time, but converts EVERY SINGLE TIME. Notice the emphasis on CONVERTING EVERY SINGLE TIME. Handlers are there to prevent throwaways. Not to be flashy.
Your best handlers are the players who:
Don't throw it away.
Make the best decision—which involves not throwing it away.
Your "best thrower", in comparison, might be the person with the buttery-smooth throws, fakes so convincing defenders jump out of their shoes and fall over, and casual 80-yard flicks. But, if that person is constantly throwing it away, they're a liability more than a handler.
Sometimes teams have to put their “best thrower” in a position to move the disc downfield, and attack spaces which other throwers cannot. And this can happen when the defense is aggressively playing the thrower and the other throwers are weak, especially with respect to distance (and somewhat accuracy). But that doesn't make that player the best handler. In the same way that Point Guards in Basketball are known to be great passers first, and shooters second, while Shooting Guards are more often better shooters than passers (at least, before Stephen Curry, my GOAT).
But, your handlers are the ones who make the best decisions and have throws good enough to execute those decisions. Sure, there's a sort of "minimum threshold of agility" to be a good enough thrower to execute good decisions, but at the intermediate-and-below level, most would-be handlers are hampered by their lack of vision, not by the size of their repertoire.
Vision is the ability to properly evaluate the field. And this, unfortunately, is largely a skill that's hard to develop without either a fantastic ability to recall the field positions with remarkable accuracy, or the will to watch game tape and take (good) feedback. Finding that good feedback—or even evaluating the feedback itself is also hard. Still, at the end of the day, watching game tape is good, and even if everyone is inexperienced at evaluating, the field, an open but inquiring attitude goes a long way.
So, the next you're wondering who should be handling, consider that "boring" player who isn't flashy but never throws it away. It might very well prove to be a better choice than the cocky guy who calls himself the "primary handler", that happens to have above-average throws, but who throws it away like 30% (or, god forbid, 60%) of the time, demands the disk, claps his hands, yells at everyone else to be chilly, but leaves you thinking: "Dude, follow your own advice."