I 100% agree with this assessment. Though I disagree that Geisler arguments in Chosen but free are very persuasive. Here's why, they never can answer with total satisfaction on Biblical grounds of how a sinner is saved before a Holy God. They can dance around it, avoid it, or blatantly misrepresent the truth for lies. Grace as you correctly stated is the remedy for sinners, and without it nobody will ever be saved, no matter how they try to twist and distort scripture. But to understand Grace one must understand why they need it, right? Our fallen wills in Adam is now in enslave to sin; willingly; by free choice; is a Mt. Everest they can't climb.
And those who read his book Chosen But Free, as you also have stated correctly need to hear the Reformed View on the matter. But if we avoid the elephant in the room as they do, how does that help us? Sharing the Biblical truths is what we must do, which includes our wills, choices, masters we serve.
15 What then? Are we to sin because we are not under law but under grace? By no means!
16 Do you not know that if you present yourselves to anyone as obedient slaves, you are slaves of the one whom you obey, either of sin, which leads to death, or of obedience, which leads to righteousness?
17 But thanks be to God, that you who were once slaves of sin have become obedient from the heart to the standard of teaching to which you were committed,
18 and, having been set free from sin, have become slaves of righteousness.
19 I am speaking in human terms, because of your natural limitations. For just as you once presented your members as slaves to impurity and to lawlessness leading to more lawlessness, so now present your members as slaves to righteousness leading to sanctification.
20 For when you were slaves of sin, you were free in regard to righteousness.
21 But what fruit were you getting at that time from the things of which you are now ashamed? For the end of those things is death.
22 But now that you have been set free from sin and have become slaves of God, the fruit you get leads to sanctification and its end, eternal life.
23 For the wages of sin is death, but the free gift of God is eternal life in Christ Jesus our Lord.
Believers have been regenerated made anew now having the ability to trust and believe in God. We also now have the ability to perform good works of righteousness because we have been set free from sin and have become slaves of God. God doesn't believe for us but he has opened our eyes, ears, hearts and minds to trust in him and follow and obey him. Because now we are new creations in the Spirit.