Would it be wrong to say that "mercy" first and foremost is a matter of me being and acting the way I believe I should be and act because it is the Christ-like way to be and act, and then only secondarily considering whether my mercy toward another is good for them? For example, would my mercy toward them be "useless" if it didn't necessarily result in remorse and repentance? I don't think so.
Well, mercy as such is good for them, regardless of whether they obtain the good we seek for them. And, too, being Christ-like is good for us, whatever effect it has on others.
I think we are, generally speaking, too concerned with questions of utility, with what is desirable because it is useful rather than with what is desirable in itself. It's understandable, since in this life we can only imperfectly obtain what is desirable in itself.
But if we only understand mercy, say, as something useful -- to us, if to no one else -- then we don't understand God's mercy, and we can't really be merciful as God is merciful.
Because mercy is of no use to God. It's just what He does. We benefit by being merciful, because we are imperfect and being merciful toward others brings us closer to perfection. God, though, is already perfect. He didn't gain anything by sending His only Son into the world. He can't gain anything; there's literally nothing for Him to gain, Who created all things.
Jesus' prayer to forgive those who crucified Him didn't make Him a more perfect Person; strictly speaking, "more perfect" is an oxymoron, even for a Being Who isn't Eternal Beatitude. But it was part of the perfection of the humanity He assumed.
We tend to focus on the process, but I think keeping our final end in mind -- to be merciful as our Father is merciful, to be perfect as our Father is perfect -- would make our mercy more Christ-like by emphasizing both the selflessness with which we should act and the sheer grace of the mercy God has shown us.