I've seen many umpires that put a number after each called pitch. It was generally an after-the-fact type statement - there is a slight pause between the designation of the pitch and then a following number.
We've got a very good, veteran umpire in our association that actually sells the THREE part of the call - his strike call is nearly the same as any other strike call and the THREE is emphasized. Don't know that it is right or wrong but that is what he does.
Personally, I don't use the numbers. My strike three doesn't even resemble a word. When you hear it, you know you're done. Humorously, I've only done a very few little league games and then I had to intentionally tone it down out of fear that I would scare the kids and make them cry.
I state the count often. The battery and the batter should always know the count - even if I don't say it. I state it often primarily so I can remember it (no idiotclickerthingamobob). But there is always the fence post, I mean coach, that is not even looking towards home as you are showing the count, that asks, "What's the count, Blue." And of course the deaf catchers who will also ask within 2 seconds of you just stating it.
Duh!
Strike calls should just be matter-of-fact. They are not ever to embarrass or show up the batter. Perhaps the veterans, of whom you are speaking, feel the use of a "number" may be showing up the batter (strikes) or possibly the pitcher (balls).
Little League probably needs to make it a requirement.
There are those kids that just stand in the box until either the umpire or the coach tells them they are done! "Nice job. Now hurry down to first... no that's third. First is this way. Good job! Way to watch those pitches."