ok,let's reverse the argument. what if we privatize national defense (something i would not support for obvious reasons) but just for the sake of argument.
how would individuals "consume" national defense?
me, personally - i would have no idea that i would need to purchase one contract of "keep that Taliban idiot from killing me this month" or i'll take one of those "North Korea whacky missle 'who knows how far its gonna go this time' anti-missle" things.
on the other hand, it is much easier for an individual to "consume" healthcare and in many, many cases to "overconsume" healthcare. if we nationalize healthcare, i can see a case where parents will be taking their kids to the doc everytime a sniffle pops up - heck they already do and hospitals write off gazillions of bucks in non collectibles each year. ER's after 5 pm get a boatload of business and most are not allowed to refuse service - some federal law thingy.
before i had decent insurance for my family, my kids had to be beyond the "well, he's slightly blue, but i think the color is coming back" stage for us to go see the doc. a little over the top, but hope you get my point.