If miracles and resurrections are a crutch for the faithless, why did Jesus need to be publicly resurrected at all? [...] Why should the people who had rejected Jesus's teachings when they heard them get the encouragement that the rich man was refused? Why should Paul get a personal appearance from Jesus on the road to Damascus, when his colleagues were allowed to go on persecuting the Christians?
The Resurrection of Christ, at least, is not a counterexample to the parable. The Resurrection is not merely a sign that Christ has conquered death, but the very fact of that victory. It's not as if Christ's resurrection validates his message, and encourages us to take him seriously (though this is true to a certain extent); rather, the Paschal drama is itself the reason for the Incarnation, and the Resurrection is an integral part of that.
This is not the case with the resurrection of Lazarus (and with other miracles). One traditional understanding of Christ's miracles, however, sees them not as prodigies performed to compel unbelievers into belief, but as symbols that reveal something about the nature of what we believe in. It's worth noting that almost all Christ's miracles are performed for people who already believe; in fact he refuses to perform any miracle when a sign is demanded of him.
In point of fact, I don't really think that too many people are convinced by miracles. The miracle of the sun at Fatima was witnessed and testified to by all manner of atheists, but they generally managed to find some explanation for it that didn't require the intervention of the Mother of God. For all we know, there were a hundred Sauls of Tarsus who were struck temporarily blind on the road to Damascus, and only one who resisted the temptation to write it off as heatstroke or attribute it to those sketchy-looking kebabs they'd eaten along the way.
This is what Christ means when he says that signs will not convince those for whom the law and the prophets are not enough. And on that note, I will tell a parable (it's been presented as history, but I'm not sure whether I believe the source):
Émile Zola, in an anticlericalist mood, decided to make a trip to Lourdes, to record, in his characteristically realist style, what was to be observed there, and to assemble it into a critique of French Catholicism.
Lourdes provided him with plenty of ammunition for that, and he reveled in the place. There were the innumerable shops and booths selling kitschy religious images and dubious relics; the hucksterism of the preachers; the multitudes of sufferers preferring, in their ignorance, magical water to modern medicine; and the waters themselves: frigid, brackish, and contaminated with the pus and blood of a million pilgrims.
There was more than enough in the grottoes of Lourdes to satisfy Zola's taste for grotesquery. And in the interest of narrative drama he sought out the most pitiable case he could find. There was a woman afflicted with lupus; her face -- on the few occasions she raised her veil -- was a nightmare of running sores and swollen flesh, and she had come to Lourdes out of desperate hope that the Virgin might cure what her doctors could not.
Zola pointed at her the triumphant finger of doubt: "I will believe," he pronounced to the pious doctors in attendance, "when this woman is made beautiful."
And of course it came to pass that when the poor woman took to the waters, her disease began to show signs of improvement, and she grew healthier with each day. The pious doctors could find no medical explanation for this cure, and they brought the woman to Zola, pointing the triumphant finger of faith: "M. Zola," they said, "you who would test God: behold! she is cured."
And they showed her to him: her sores had ceased to run, new skin had begun to grow over her lesions, and the swelling in her face had subsided enough that one might see her smile.
But Émile Zola averted his eyes, and said only: "She is still too ugly."