The VA actually operates in competition with other health care providers since the rules were changed and only those with service related injuries and those without other insurance can be treated without being charged for their services.
So you can’t compare the VA to Canada’s or Britain’s socialized medicine.
And actually the VA focus has been, in the past, on increasing patient satisfaction so that those who DID have other coverage would choose the VA, increasing non-governmental revenue. However, since the economy has become increasingly wrecked there has been an influx of patients into the VA with no insurance coverage. This is increasing the strain on the VA causing delays in care... which is exactly what would we see if the VA were converted into part of a universal health care system.