Your points are valid. The investigation should be funded by bicycle companies that stand to gain from such improvements. I can see no role for taxpayers in such a study.
And those bicycles are already made by a lot of small companies. Bikes for the 350+ pounders, bikes for people with back problems, bikes for people who can’t use their legs, bikes for people with balance issues, etc., etc.
Others would say that it is immoral for such advances to be monopolized by a single company, keeping everyone except that company from benefiting from the research.
In my experience, companies do only research that has a clear potential for profit, preferably in the short-term. Government funded research tends to be more open and ask the basic "how" questions that lead to the basic mechanistic understanding that allow companies to develop the profitable products. I am a basic scientist; the things I do in the lab typically percolate to the commercial world a decade or so after they become commonplace in the lab.