Does God know people? I mean know them, as in what truly motivates them, what their secret desires are, what is the likelihood they would do anything in a particular situation. I think he does, and does so with astonishing acumen (he is God after all). It is obvious he knows their histories, including every overt thing they have either said or did and every secret rumination of their hearts, but he also sees there entire life at once. I think it is beyond doubt that he would know how they would respond to efforts he would make to coax them, inspire them, persuade them, command them, or otherwise engage them.
If God is so thoroughly familiar with people as I've suggested, is he under any obligation to attempt to rescue those he knows would only rebuff his efforts? If Jesus has any thing to say on the subject, I think his answer would be a resounding "NO." Folks who would pay no never mind, are not guaranteed to get the opportunity. His instructions to his disciples above seem to bear out this principle.
If extra-biblical history yields any insight into the question, it too, I think, offers a resounding amen to the proposition. Vast swaths of human population have come and gone without ever hearing the Gospel. Of those that have, vast swaths ignore it outrightly or pay it nominal fealty at best. Hopefully, we all realize it is not the hearers of the Gospel that are saved, but those who believe it and follow Christ as a result. Given what we have seen with those who do hear the Gospel, there is nothing to suggest that even some of those folks that have not heard would have responded to Christ with faith had they heard.
Pointing out these kinds of things can cause folk who believe in the inclusivity of God's love and the universality of Christ's atonement (as I do) to be aghast. In my mind, some of these posit a sentimental notion of God's love that doesn't reflect the evidence of life in general nor the scriptures in particular. Just because God would rather see someone saved than lost, it cannot be inferred that he has an obligation to try to save that which cannot be saved. As for me, I think God knows what he's doing without my counsel or condemnation, and that everyone who would have been saved will have been saved when all is said and done.
Let's say, for the sake of argument, that God has bound himself to giving each person, by some means, a personal opportunity to receive or reject Christ. If the result of people known to have actually had that opportunity produces, proportionally, so little fruit, how would the outcome of some extraordinary effort by God to reach them ex-gospel be significantly different? Without the Gospel they do as they want, oblivious and uncaring about God's desire. With the Gospel they do as they want, dismissive and uncaring about God's desire. Why think that there was some untapped potential among the unhearing masses that would have responded if it would have had the chance?
Who could fault God if he decided to bypass the rigamarole and cut to the chase? Could we trust him with that judgment? Rather than posit extra-biblical, feel-good notions about partial grace/partial revelation, or post-mortem grace, or universal enablement, or whatever (none of which have anything close to definitive statements in the scriptures to support them), why not say what we can say clearly and leave judgment in the hands of God? Rather than pretend to know how God graces or judges, leave it to God and say no more than he has said. Regardless, nothing justifies suggesting there is something other than the Gospel that saves.
As for me, I see no way in which God is obligated to cast his pearl before swine.