This is an impressively bad idea. Some private insurers might insist that veterans get treatment "in network," and the VA specializes in the care of service-related injuries, while many contracting hospital facilities do not. This could compromise quality of care.
Further, this would not "save" a half billion dollars - it would merely transfer the cost to the private insurers, which would therefore have to raise their rates to cover this new cost. The results could be especially devastating to self-insured employers who lost the service of their loyal employees to the military, and then got socked with a big bill for treatment of war- or service-related disabilities.
Congress has apparently already rejected this idea. Good.