Even with a 2/5 vs 3/4, Mandarin/Witch is still worse than Witch.
When you play Witch, you end up with a 6 card hand. At $.7/card that is an average of $4.2 which is not bad odds of hitting $5 on the next shuffle. If it were absolutely vital to $5 you could open Witch/Copper and you'd expect to hit $4.8 on your witch turn.
The fact that opening Witch/Copper is almost always inferior to Witch/- speaks to how unimportant hitting $5 again after Witch is.
More often if you'd actually care enough to delay Witch, you'd just buy the other $5 instead (say Count or Tactician) and get the Witch later.
Going Mandarin doesn't really get you back to $5 sooner regardless - you start one turn down and a Witch deck is 2 cards faster than a Witch/Mandarin. If the Witch needs to buy two Silvers, well so be it. She will get them shuffle in after T4 and will have her first chance to play the new $5 on T7.
Witch/Mandarin will get a chance to buy on T4, and might draw it on T6 (though with an effective deck of 12, only 3/5 slots are open to hit the new card).
Courtyard is very good at BM, because BM really values cash smoothing. Being able to move a copper off a $7 onto the deck top makes it much more likely you will $6/6 than $7/5. It only gets better late game. Late game, when you really want province, it is very effective to send back golds to increase treasure clumping. You'd often far rather hit $8/2 than $5/5; and even when you'd prefer 5/5 you can do that. Courtyard gives you a lot of end game control for BM and a lot of price smoothing - very nice for its price point.
Mandarin is a slow start and just is as powerful early.
In general, BM is of limited utility in measuring card strengths. It highly undervalues trashing and sifting. Cards that are priced cheap (e.g. Smithy) are better than a LOT of expensive cards (e.g. Hoard, Harem, Treasury, Market, Horn of plenty, Expand). Money smoothing is nice, but often it isn't as nice as faster cycling.
Again neither Mandarin or Courtyard are bad, it is just that their balance is toward different things. Mandarin is much better when draw is "easy" and Courtyard is much better when draw is "hard".
