So, there's a few things that I'd like to clear up about the nature of kamikaze pilots. Kamikaze attacks were not conjured due to Japanese fanaticism, they were created as the result of Japanese desperation. The difference between the two gives us insight as to what and how the kamikaze tactics developed and what an individual pilot might be thinking.

To begin with, most kamikaze pilots were not actually trained in aviation combat. That was the whole reason they were kamikazes. Attrition and a strict training regimen had wiped out the core of skilled pilots that Japan had relied on for air combat, with the heaviest losses being accrued among the torpedo bomber and dive bomber crews. The reason for this is simple: fighters typically were not expected to dive into the effective range of anti-aircraft guns, and Allied interceptor doctrine, like most navies, prescribed destroying attack aircraft before escort fighters. Allied air defenses were incredibly powerful: the use of innovations like the proximity fuze, combined with the low armor of most Japanese planes, rendered flak extremely effective. Thus the Japanese found themselves with a major deficit in airmen to attack ships, and none could be trained easily. This was the environment in which the adaption of the kamikaze idea was incubated.

People like to point to the Japanese "code of bushido" and their fanaticism to the emperor as to demonstrate their willingness to adapt this tactic. But the truth is there was no shortage of doubters among the IJN, including many who thought that in addition to the disgusting waste of life it was also a poor use of military resources. What is the point of building planes and training pilots that don't come back? This tactic was not just for planes, either-the Japanese developed torpedo boats that were really just designed to ram Allied ships and explode, they trained frogmen to dive under and set charges to ships, and other techniques that we now associate with either religious fanatics or "brainwashed" soldiers. But this was all done because the Japanese had no way to competing with the powerful industrial giant that was the US war industry. They had to compete in some way. Economists would frown on using one of the basic theoretical models-the model that Production is directly dependent on some amounts of Labor and Capital-but essentially lacking the "Capital" component, the Japanese chose to increase their "Labor" share. At great cost.

Now, to actually get into the intricacies of your question-of course the Japanese would allow pilots to abort their missions. If we pretended that these kamikaze planes and their pilots were just regular planes, we would think many such actions would be common sense. For instance many kamikazes returned to base due to mechanical failures. Japanese engine production quality was always rather questionable, more so during the latter stages of the war, so this was unsurprising. There is no point wasting this pilot and his plane by making him crash into the sea for no reason. If you could, you would have him return to base, fix his plane, and send him back out again. What's the point of having him continue and crash into open sea without an enemy in sight?

As for people who intentionally shirked, you have to understand the vast pressures being placed onto people who were volunteered-or perhaps we could say coerced-into doing this. Japanese social pressure is an extremely powerful force, one that Westerners are not nearly as familiar with. I cannot emphasize enough how powerful this peer pressure was. Essentially, even if individually nobody wanted to die, collectively they were afraid that if they tried to shirk their peers would look down on them. They were also given alcohol before their flights, supposedly as "liquid courage" and "good luck" but it had the side effect of relaxing the pilots and making them less likely to resist. Lastly, the truth is that many pilots were in fact willing to die-but not for some emperor that they had never heard of or from some warrior code from ancient times (incidentally, Bushido itself is a modern construct, but that's another story)-but instead because they saw the bombs that were being dropped on their homes and families, they felt powerless to help them and stop the Allied advance, and felt that this was the way in which they could contribute the most (short term, at least). Many of the pilots were college students, so they were educated to at least some degree. The Japanese government originally shielded them from the war as they would be more useful once they had completed their education. But they needed the most hands on deck "now," no matter the cost in the future. It was a war of survival to the Japanese, not just a war like we see it today.

Sources:

Dower, War Without Mercy
Saburo Ienaga, The Pacific War
Ohnuki-Tienrey, Kamikaze Diaries