CR can help the opponent.
But it helps you a lot more.
Engines typically buy a lot of cheap cards in the early game and draw the entire deck anyway in the late game. If the opponent already has a hand which will result in drawing his entire deck, the +1 card for him means nothing. If the opponent already has a hand which will result in getting the engine piece he's going to buy this turn, the +1 card for him means slightly faster cycling and nothing more.
The big money player wants a lot of expensive cards such as Golds and Provinces, and will never draw his entire deck no matter what. The 4th card you draw from CR has a significant chance of getting you over the $8 threshold, or the $9 threshold to buy Gold+Silver, or the $11 threshold to buy Province+Silver, or the $12 threshold to buy Gold+Gold, or the $13 threshold to buy Province+Duchy, etc. Not all of these are useful compared to a lower price point in all situations, but very often, even a single +$1 can enable something better than what you otherwise would have had, and at the very least, it removes a Copper from your next hand. The worst is probably getting a Silver to get you from $8 to $10, but even that allows you to buy an extra Estate in the late game, or the Gold+Silver rather than just Gold in the early game, or double Duchy in situations which probably will never happen against an engine. These are
significant changes, unlike the "cycle 1 random card" that your opponent is getting.