Well obviously some parts of pieces are sight readable hands together...
"if you are trying to overcome some specific technical challenge, isolate a voice, or trying to memorize a score, then HS is indispensable" ....
That pretty much sums up why you'd want to start a piece hands separately.
I'm just starting the Prelude and the Gigue from the Bach G minor English Suite. I don't think I'd be doing myself a favor learning either of those hands together (even though there isn't a technical hurdle in either of these). In the Gigue especially, I would not be giving close care to the left hand fingering and would probably end up having lots of awkward jumps and a huge lack of legato.
That's one of many examples why I'd personally not jump into a piece hands together; but, if I were to take something like an easier Chopin Prelude for example, then that would be a case where I'd be very comfortable learning hands together at the start.
It really depends on the piece, but there's no universal YES or NO whether you should learn pieces hands separately.
Another example would be the Fantasie Impromptu; some n00bs try starting that piece hands together with a bad understanding of poly-rhythms. If they were to try each hand on their own, and understand with a metronome the pacing for each hand, and where they'd be playing at the same time, then they just might not say "holy sh!t" at measure 1.
I don't know, some people I know say "what's the point in learning the piece twice, when you can do it once hands together"... that kind of hints they want to get the piece over with, and think just doing it once will get them through it.
Those people need to consider that learning it "just once" will probably take about as long as "having to do the piece twice", if not longer. Getting through it with only the right hand lets you focus just on that... why would you add the left hand when you haven't seen what the right hand is throwing at you.
that example is purely hypothetical... and again, I'm not saying you need to play Jingle Bells hands separately

; but, in the long run, if you figure all of the basics out and not just start sight reading super sloppy hands together, then the end product will probably sound much better.
My long posts always turn into rant-form and at points probably don't come out very clearly
