What would be wrong with posting air miles to the company account? It seems like an extremely logical and good thing to do to me, and I don't understand why airlines would want to discourage it.
It would remove the incentive for employees to pay $2k of company money to get $100 worth of (personal) free stuff.
Why would car rental companies (or airlines, or hotels, or anyone else in the travel business who noticed this particular quirk of how businesses conduct travel) want to discourage this? It doesn't help them at all to make this change, and would likely seriously hurt them.