Hi Johnny,
Yes, you are right. We are indeed very fortunate indeed.
Many people still think anicca means impermanence. Yet many things do not perish within the span of a human lifetime. Mountains and rivers are such examples.
The meaning of inconstancy would be closer to the mark. For even during the timespan that they are in existence, they are subject to unexpected change (viparinama). For example, the waters flowing through a river now are not the same waters that flowed through it minutes ago. Exactly which waters flow through depend upon any obstacles that lie in the path of the waters upstream, such as pebbles and rocks and whirlpools. Rocks and pebbles can also be eroded, leading to the formation of new obstacles or to the removal of existing ones, which further affect which waters will flow through in the future.
Yet even the understanding of inconstancy may not quite hit the mark. For example, even though we know that the waters of a river are inconstant, surely that does not bother us. It is when we consider things closer to our desires that the understanding strikes a chord within us.
Phenomena and things in this world cannot be maintained to our satisfaction in the long run. This understanding is what truly matters to us. It also incorporates the above meanings of impermanence and inconstancy, yet it goes deeper than that to what truly exposes us to suffering. (For our wrong views that things in this world can be maintained to our satisfaction in the long run if we just put in enough effort are so pervasive, insidious, subtle, disempowering and restrictive that just accepting the meanings of impermanence or inconstancy alone would not be sufficient to shatter these illusions.) When we understand this deeply and intimately, we will stop being so depressed with the unsatisfactory nature of existence. We would reduce our craving and grasping, our longing and aversion, our fears and anxieties. We will start to see the futility and danger of clinging to anything in this world. Then we may glimpse the benefits of searching for and embarking on a way out of existence.
Many people also think that anatta is not-self. The Buddha stated that there was not any Self in rupa, vedana, sanna, sankhara and vinnana. However He did not just state that. He also stated that these things were subject to unexpected change and could not be controlled. Therefore, I like to think that anatta does not just mean not-self. It also means something that is without control and without any abiding essence. As such it cannot offer any refuge and cannot deliver us from suffering. Surely it is better to have a more general, all-encompassing understanding than just a specific one that may not be applicable to all cirumstances.
This is what I understand.