The best form of education is to learn from mistakes. That is the essence of science and arts. Unless we create an imperfect something, we never realise the value of the real perfect. However, cost of imperfect creation is high and thus we must try to minimise this cost. So, I understand that the smart thing to adopt is to first learn from mistakes of others and then embark on the creating something new. In this process, we will still create something imperfect in the beginning. However, this will be much closer to the perfect form.
For a society to progress towards being in the ideal state, it is very important to remind the society of the past – the good and the bad. The good should be repeated and the bad should be eliminated. The place where the society preserves this invaluable knowledge is in the museums. While it takes a while for a child (or even an adult) to grow up to appreciate the lessons hidden in the museums, ultimately every human being searches for these lessons for improving his/her life and the lives around him/her. Generally, these times of searching for solution comes after the human being has undergone the worst experience in life.
So, while a sports arena would give immediate pleasure and would serve the immediate needs, it is actually the museum (which will be far less used), which will give greatest value for the people and for the society. So, in my opinion, the public authorities generally have no pains in deciding in favour of building museums over any other utility, even after knowing that the revenues generated from creation of the museums will never be a fraction of what any other commercial utility can generate. However, everywhere in the world, every public body build these museums and mostly fund it entirely from public money with or without any income from them; as the intrinsic benefit of the museums is just invaluable and eternal.