What do other apologists say?
C. S. Lewis in The Screwtape Letters tried to explain it this way: “[God] cannot ravish. He can only woo,” but this relationship analogy fails. In an ordinary human relationship, the very existence of the other person is never the question. No party to a relationship “ravishes” by simply making their existence known. The rare examples where someone is fooled into believing someone exists become man-bites-dog stories. (Consider the surprising story of Notre Dame football star Manti Teʻo.)
Augustine had similar advice: “Do not understand so you may believe; instead believe so you may understand.” But why? You don’t pick a belief system first and then select facts to support it; it’s the other way around. You follow the facts to their logical conclusion. Christians are forced to imagine a trickster god who plants vague clues to the most important truth.
What does the theist admit when using this argument?
Consider the theist’s desperation in advancing an argument like this. For any reasonable claim of existence, we are given evidence. You want to know what “the sun” is? Just look up on a sunny day. You want to know what a black hole is? That’ll take a lot more effort, but there is plenty of evidence for black holes, too. And yet for God, we get just a suggestion of a shadow. If God loved us and dearly wanted us to know him, he would make his existence known. He doesn’t.
So—option B—we assume God’s existence and say that he wants to be an enigma for reasons that are unknowable to us. But, of course, if he wanted to be hidden, he would be so! If you’re playing hide and seek with God, you will lose. He’s God—he could leave no trace, and there would be no enigma.
That leaves the Christian with option C: God isn’t deliberately hidden but instead leaves just the vaguest of clues—only enough to tease the seeker. This is rarely enough to give complete confidence, so the Christian is always on edge, never quite sure whether he’s got it right or is instead going to hell. This is a god who plays games with people’s lives.

See also: How Reliable Is a Bridge Built on Faith?

So where does this leave us? A God too shy to even make his existence known contradicts a God who wants a relationship—he can’t be both. Koukl’s handwaving about how people would respond to an obvious God (lots of people would still disbelieve; they’d have their own selfish reasons for rejecting God) ignores the fact that this would remove the legitimate obstacle of too little evidence for millions or even billions of people.
And how hard would it be for God to make everyone believe he exists? I could convince any sane person that I exist. Can’t God do the same? If I can do it, couldn’t an omniscient god a billion times smarter than me do it, too?
Koukl might say that God’s hiddenness doesn’t prove that God doesn’t exist, which is true. But it certainly gives us no reason to believe in him. We can’t prove that God is nonexistent, but he’s functionally nonexistent.

Man to pastor as he leaves church:
“Oh, I know He works in mysterious ways,
but if I worked that mysteriously I’d get fired.”
— Bob Mankoff cartoon

Image credit: Dong Jun, flickr, CC