i don't think Hershel's attitude toward Walkers is all that unreasonable.
For one, he's a man of faith. He already belives in the dead rising. But now that it's happened to millions (which, by itself is a "miracle"). Why is it unreasonable that he'd believe a cure was possible? His is a religion of hope
and new life.
Also, he mentioned what he saw on television, and how brutal that was. If anything was caught live like what we saw in flashbacks, Herschel may have also wanted to take a different view to not be like "those guys."
i can imagine that he saw infected-but-not-dead people being shot brutally
shot by police or some other "authority" . Those were people who not only considered Walkers not human, but also lost their compassion for even the dying. If that's what he saw on TV.....
On a different note. If we're assuming that everyone has the Zombie virus, that when you die, you become a Walker... one of the "side effects" is a regenerative power that works for most injuries (like gun shots & arrows) , but not against the Zombie killer bacteria. That's how a guy who was in a coma & dehydrated can make it out alive, or Carl & Daryl recovering in 2 daYA or Merle making it out... That's my quasi-serious fan theory on that.