The effect does matter even without fatigue. You gain information and knowing things you don't need to play around anymore is valuable.
How useful this card is varies greatly depending on the match up but it's not useless.
People heard somethings about discard not mattering back in the fel reavers days and Kibler's essay and just parroting it out without actually considering the difference and the context.
Fel Reaver's drawback didn't matter most of the time because you were playing a face deck. The opponent you're playing this against isn't always a face deck, it can be anything. The biggest drawback of Fel Reaver in the end was information it gave away not discarding your deck. If you didn't need to play around force roar anymore, that was huge.
There is a acolyte on board, you have a chance to mill 2 cards without much effort or investment, you saw earlier that they've already played a bunch of cycle cards too, of course you go and mill those 2 cards because it's likely going to hit direct damage or iceblock or something key to your loss... Sometimes, sure if you're missing like 5 damage to mill a card on turn 3, yeah it's wrong to do it. This is what this card is, milling without that much investment. A 2/3 is not great but it's hardly back breaking, specially a control warlock with hardly any good turn 2 plays. Sure you tap against control, against something else you don't want to tap. You're playing a tech card like doomsayer or crab, consider this a 3rd option next to those with different pro/cons. You don't want to play defile on 2 most of the time.
The mindset of milling not mattering or that the card might as well be their bottom of the deck is not absolutely correct. It does matter a lot sometimes. In control mirror it's very likely going to be good. You have to be very unlucky to hit a card draw card rather than a value card as those are like 2-3 in a control deck.
Here is another case to look at. A quest mage deck needs 5 cards to do their combo. That's 5/30 on average, you win the game, you have 2 chances too if you're running 2 copy. They need 4 key cards to complete the quest itself. 2x glyph and 2x tome, that's another 4/30. Then they need 2x iceblocks to stall long enough to win. So you basically have 6/30 chance of delaying their game plan by a lot. Over 30 percent of their deck is a positive outcome for this card. So bad!
You're playing against standard miracle rogue. The way they win is that they build a board big enough faster you can possibly draw removal for. 2x giant, 1x questing, 1x Edwin, 2x Auctioneers and 2x prep to get there. That's 8 cards that are played directly for the gameplan. They have to survive against the incoming board too. You have 2x slayers and 2x evis in the deck. You basically have about 12/30 positive outcomes that give you more time by slowing your opponent down significantly
Sure against pw probably doesn't matter what you burn unless it's like a Arcanite Reaper, Leeroy, something huge like that which is unlikely.
The other factor you're not taking into account is tilt, this is a card that can annoy your opponent and push them to make bad plays.
tl;dr. the card is better than river crocolisk unlike what some might say and it will have its own niche uses depending on the shape the meta takes. It's an interesting effect to have in the game finally. I could say it's easily 3/5 at worst.