A lot of people with education in management/business do go into HR, at least in countries I know, and it does not help. People with extensive management experience would help but they will only take more senior roles.
The other qualifications open opportunities interesting and well paid careers. How would you attract those people into HR?
I am not even sure it would help if you could.
I think the suggestion in the old management book by the guy who turned around Avis that you should have an old style personnel department to do admin and advice, and managers should have more involvement might be a way forward, but I am not sure it would work given the current level of regulation (in the UK anyway - I imagine most wester countries are the same). A lot of the function of HR is to avoid legal risk (e.g. fire people according to the rules, so go through the motions of warnings etc).
What it really comes to is that a lot of people love to micromanage everything. If you hire someone that has integrity and educational background in subject, he/she will warn you if the decision you are making will have consequences in the long run. If you have someone that does not have relevant education, that simply does not happen. The managers micromanage, those people receive salaries and if they step out of the line even when they are right, they are reminded that they do not have relevant knowledge in said department (law/economy). This in turn leads to a lot of people gaining something called shallow experience which then in turns leads those people to hire someone that des not pose the risk to their position further down the line.
The problem being in this case is that there are a lot of misses that happen when the HR is organized like that; from illegal hirings, not knowing key economic factors, not having a clue about the business itself, no clue about laws and procedures and so on. Which in turn does not really protect the company because the company loses both the money and employees.