Short answer: yes—that’s a good, biblically faithful way to put it, with a few nuances.

In Scripture the sacrifices were God-given, not because He needs blood, but because they taught Israel (and us) that:

• Sin is serious and costly. “The life…is in the blood” (Lev 17:11). Taking a life dramatized that sin brings death (Gen 2:17; Rom 6:23).

• Substitution and mercy are real. An innocent life “stands in” for the guilty (Lev 1–7). That’s not pagan appeasement; it’s God providing a way to come near (korban = “drawing near”).

• Grace is free to the sinner but costly to the giver. In the OT the cost was the life of the animal; in the NT the cost is borne by Christ, “the Lamb of God” (Jn 1:29). God remains just and the justifier of the ungodly (Rom 3:25–26).

Think of a loving parent: they gladly forgive, but real forgiveness often means the parent absorbs the cost (time, money, pain) or imposes wise, restorative consequences. That’s closer to the biblical picture than “forgive with no cost.” Grace isn’t cheap because holiness and justice aren’t negotiable—God doesn’t wave sin away; He deals with it.

Key threads conservative Christians emphasize:

• Pedagogy: the sacrifices were a tutor (Gal 3:24) training conscience and community.

• Covenant presence: sacrifices maintained fellowship with a holy God (Lev 16).

• Fulfillment in Christ: repeated animal sacrifices pointed forward to the once-for-all sacrifice (Heb 9:11–14; 10:1–14; 1 Pet 1:18–19).

Also note: Israel offered grain and thank offerings too (Lev 2), but atonement required blood (Heb 9:22). After the Temple’s destruction, Jewish practice emphasizes teshuvah (repentance), prayer, and charity (cf. Hos 14:2), while Christians see the sacrificial pattern climaxing in Jesus’ cross.

So your instinct is right: grace is truly free to us, but never cheap—it cost the life of Another.