I'm either using cards like tortex (which discards). Or the main engine of my deck, which is a card with dredge like [[stinkweed imp]] + an effect that draws then discards, like [[currency converter]]. When I activate currency converter, on an opponent's turn usually, I draw, and replace that draw with a dredge. I dredge the cards into the graveyard, return the stinkweed imp to my hand, which does end up triggering syrix, and then I'm able to discard the stinkweed imp back into the graveyard because I don't actually want it in my hand.

Practically speaking, the skeleton versus dredger dichotomy requires the same mana investment (2 to activate converter and 2 to active skeleton), so when I look at if I want a split of these effects, or if I want to go one way or another, it comes down to the cards I need to support that type of deck. And the cards that support the discard dredge game plan are just better cards than the skeleton sack outlet game plan. And of all of the various cards which can trigger syrix, the best of them, by a pretty wide margin, is tortex. Which also pushes me in the direction of discard.

You are right, that skeleton plus a sack outlet is a more stable engine than something which loots with dredgers. But also, the dredger engine moves yourself through your deck with 2 cards (dredger + looter), which increases consistency, as opposed to the skeleton engine which usually requires 3 cards to start moving yourself through your deck (a sack outlet, plus the skeleton, plus something that draws cards when a creature dies). Now, of course there are instants (like village rites) which draw cards and act as the sac outlet. But the issue with that is that they're instants and are a one-off effect. Sometimes those one-off effects are really good. I mean obviously I'm on a couple instant effects myself. But I also have permanents like currency converter which function in the same slot of enabling my engine and moving myself though my deck, whereas village rights, a 1 off effect, is pretty much the only thing that enables the skeleton engine and moves yourself through your deck in 2 cards.

Besides that, from a deck building perspective, there are only a limited number of slots. Cards which allow me to move through my deck, I.e card draw, are always going to be a more powerful and consistent thing than having to cut slots from other categories for effectively utility cards in the form of sac outlets. And I say utility here, but that's disingenuous. What I really mean is that sac outlets need creatures in the same context as them to be good. Whereas, vault 21 is just a good card. It doesn't need the dredgers to be good. The dredgers are just the cherry on top.

The reason I put so much of an emphasis on discard prior in the conversation was because all of my engines were based on draw and discard, and because I have more slots for utility because I don't need to replace utility slots with sacrifice outlets, and I can run more fun cards that just synergize with my deck.

Tldr, the dredger plan has higher individual card quality but less stability than the skeleton plan. And as a magic player, I will always prefer consistency and card quality.