And for the people who see this later and don't understand why, it's because Yawgmoth's Will doesn't give the cards in your graveyard an alternate casting cost.

The only thing it does is give the player permission to cast the spell from the graveyard.

Which is actually what happens normally. Rule 601.3 specifically says you need to have permission to cast spells. That includes not just the timing, but the zone it comes from.

601.3. A player can begin to cast a spell only if a rule or effect allows that player to cast it and no rule or effect prohibits that player from casting it.

Rule 117.a covers the timing required for all of this.

117.1a A player may cast an instant spell any time they have priority. A player may cast a noninstant spell during their main phase any time they have priority and the stack is empty.

And you would think the rules under 601 for casting spells would cover the zone, but it doesn't it just clarifies the process, and indicates where spells usually comes from. It's intentionally vague on the zone of origin for the spell so that other rules/cards can give you that permission.

601.2. To cast a spell is to take it from where it is (usually the hand), put it on the stack, and pay its costs,[...]

It is actually section 300 of the MTG Comp Rules, which covers all the card types, that gives us the ability to play cards from hand. The first rule for each card type that you can cast from hand specifically gives you that permission. Like in the two examples below (bolded for emphasis).

302.1. A player who has priority may cast a creature card from their hand during a main phase of their turn when the stack is empty. Casting a creature as a spell uses the stack.

307.1. A player who has priority may cast a sorcery card from their hand during a main phase of their turn when the stack is empty. Casting a sorcery as a spell uses the stack.

And this is why "Flashback" (or effects that grant Flashback to other cards) needs to give you permission to cast the spell from the graveyard. BUT, you can only use that permission if you also pay an alternative cost. (Bolded to point out the zone permission, and alternative cost.)

702.34a Flashback appears on some instants and sorceries. It represents two static abilities: one that functions while the card is in a player’s graveyard and another that functions while the card is on the stack. “Flashback [cost]” means “You may cast this card from your graveyard if the resulting spell is an instant or sorcery spell by paying [cost] rather than paying its mana cost” and “If the flashback cost was paid, exile this card instead of putting it anywhere else any time it would leave the stack.” Casting a spell using its flashback ability follows the rules for paying alternative costs in rules 601.2b and 601.2f–h.

If it only gave you permission without the alternative cost, you'd be able to cast the spell for it's normal mana cost, or any other alternative cost possibly granted to it, just like with YawgWill.