Ehh I have used the sifting quite often. First there are the obvious combos: Bustling village, Swashbuckler (if this or Lib came out of the BM deck), Mountain village and the like.
Then there is the utility of balancing your draw. Mv is an extreme example of this, but in general, you want to draw villages before terminal payload. With Mv you can use all of your draw slots to hit Mv and then pull payload out of the trash. Two Libs can draw 14 cards which lets you hit say 6 terminal payloads (e.g. Gladiator, Animal Fair, Count, Goons) and this is much more likely if you don't have to waste say 2 of your first 4 draw slots on payload you might be able to use. I will routinely skip my terminals to hit my villages on the first run through and then draw all of them on the second. For some setups this is just crazy more efficient (e.g. Native village is much more valuable if you can play 6 in a row than having to use 1/2 to take something off the mat or risk stranding one of your villages for the turn). And of course there are things like Golem/non-terminal (e.g. Golem/Candlestick maker) where you pretty much always want to dump non-Golems to play more Golems. And sometimes your "village" needs a specific combo (e.g. Horse + Procession) and you benefit from fishing for one component over the other.
Then there are combos were order matters. Skipping your Masquerade to draw & play the Militia first is often a far superior move. As are things like getting down Priests before other trashers (e.g. Priest/Fortress/Junk dealer), Liveries before gainers (e.g. Iw/Livery), or attacks before Soldiers.
Then there is the whole defense against useless actions. Ruins for instance. But also actions not worth playing any more (e.g. Chapel) or too dangerous to play (e.g. Hermit with piles approaching).
This is all sifting in some fashion. And I do something from this list most every game (the most common being flipping a terminal in hopes of hitting a village I need to play the terminals already in hand).
If you really want the value of the sifting to be clear, think of a Village/Goons/Donate/Advance setup, you will have no non-actions, treasure is pretty much useless for bootstrapping, and you want lots of efficient draw: would you take Scholar or Lib for your draw? The sifting makes this no contest for me.