Hi Akvan,
As you said, the Buddha’s Enlightenment did not remove his bodily pains. The suffering that is removed at the Buddhahood (or Arahanthood) is the future suffering.
The body that the Buddha had was a result of previous causes. Those causes had already yielded results and they cannot be fully stopped. Once a sankata arises due to causes, then that sankata (in this case the physical body) will run its course.
The mental pain that you talk about in the fourth paragraph is “samphassa ja vedana”. That is not due to previous causes. Once one attains Arahanthood, “samphassa ja vedana” is stopped too; see, “Vēdanā (Feelings) Arise in Two Ways“.
Of course “samphassa ja vedana” includes elation or “mental happiness” too. They are both mind-made at that time due to avijja one has at that time.
You said, “.. If one must believe in the 31 realms to see the truth about suffering it may not be very practical. Because if it were the case then we would need to try and prove the existence of such realms without any doubt before getting along on the path.”
You may want to think long and hard about that critical point. It is very clear that the 10 types of micca ditthi includes that view. Unless one realizes that there are other realms (especially apayas), then one may still not have removed micca ditthi. The whole point is that there is much suffering in future lives and most of it is in those lowest realms; see the comment that I just made in another discussion: “Micca Ditthi“.
The existence of other realms may not “provable” by today’s scientific standards. But when one comprehends Dhamma at deeper levels, one will realize the truth of that.
Let me give an example. When the Buddha said there are innumerable “world systems” (meaning uncountable planetary systems like our Solar system), there was no scientific proof. In fact, even 50 years ago, science knew about only a handful of planetary systems like ours. It is only within the past 10 years or so that scientists have accepted that there are an uncountable number of such planetary systems.
So, we need to find the truth WITHIN Buddha Dhamma. We cannot rely on science. This is a key point that I am trying to make. When one builds faith (not blind faith but faith based on one’s understanding of Dhamma), one does not need any outside “evidence”.
This is why the Buddha said, “the world has not seen this Dhamma before”. It is a Dhamma or a “world view” that is not described anywhere else. Trying to prove those concepts using scientific evidence would not work. Science has discovered only a fraction about our world and that is limited to knowledge about matter. It knows virtually nothing about the mind, as I explained in this new post (science says this is the only life that we have, which is ucceda ditthi).
Of course, it is up to each person to decide for himself.