Logistically, considering that forward/back/up throws send the opponent toward blast lines while down throws bounce them off the ground, it only makes sense that dthrow is the combo throw for many characters - ergo, dthrows are a popular throw. Bthrow tends to be stronger than fthrow for reasons already mentioned by someone else, in terms of both damage and knockback, but depending on facing and stage position it doesn't always make more sense to bthrow over fthrow.
But, largely, it's character dependent.
use uthrow for starting combos;
among others use uthrow to kill;
has an easier time landing kill combos off fthrow than dthrow due to less time for the opponent to react and DI and sliding during the throw off a dash grab,
also has combos off fthrow,
have fthrow>Crescent Slash with customs on,
kill with fthrow...for the most part fthrows are just for positioning though.
I can probably do a better job at explaining why you see certain throws more with a more specific character example though, so let's take
. You'll see Meta Knights use dthrow a lot, because it sets up for both damage-racking and kill combos. Bthrow is his only throw with a horizontal launch angle (fthrow launches diagonally upward) and is tied with uthrow for his most damaging throw at 10%, so it's the throw of choice for getting the opponent offstage. It also leads into dash attack combos at low percents. If he grabs an opponent right at the ledge, facing the ledge, he has no combo followups and no throws that send the opponent horizontally forward; uthrow is then the throw of choice for building damage and not throwing the opponent back toward center stage. Uthrow also serves as a kill throw - particularly when below platforms, as Meta Knight will land on them before throwing - and the descent's hitbox also lets him kill off Luma/pikmin with the throw. Fthrow only combos into Shuttle Loop, but it's much more reliable for it than dthrow is due to the faster throw animation giving the opponent less time to DI, and as a bonus it does 2% more than dthrow. Point being, all of Meta Knight's throws have a use, it just depends on the situation - and it's the same for many other characters.
tl;dr - It depends on both situation and the character, dthrow and to a lesser extent bthrow merely tend to be the better/more applicable throws for many characters.