Health, there are numerous organizations and country and state leaders, I am sure at least some of them are interested in this. Lack of proofs was not surprising a year ago, but it is suspicious now.
To support somewhat your position – look at heterogeneous boosters. Every manufacturer organized trials for boosters using their own vaccine, but it was left to a university to test boosters between different vaccines. And all they were able to do so far is to test antibodies in the lab. So, yes, yetzer hara of profit and organizational biases are a big motivator. But what is the alternative? Note that Chinese and Russians vaccines are not doing better than Western.
Still, organizing a test of very cheap treatments applied in mild cases seems to be (relatively) easy.
I can’t believe there is nobody to do that.