First, Libertarians support a limited government.

We support a government for the sole purpose of protecting already existing rights, NOT to provide rights.

Second,

would not corporations and oligarchs fill that power vacuum

They very much could, but, and this is a big but, they would have to obtain that power voluntarily. Any power that they get from us, we must first voluntarily give it to them, and at any moment each one of us could very easily take it away.

Money is power. The only way a corporation could obtain money is if you give it to them. They cannot tax you, they cannot steal from you, they cannot force you to use their products/services, and most importantly they cannot stop anyone else from offering the same products or services to you.

But theoretically, one corporation could become huge and end up being 80% of the entire market. But that would have to be one good corporation that offered great products for very reasonable prices. Or else we would just get our products/services elsewhere.

Also, without the government being involved in regulating/promoting commerce, every business that has relied on the government to protect their monopoly or any company that rely on the government as their largest client will have to now convince the citizens to give them that same amount of money. This alone will cripple a lot of huge corporations, no more government contracts, no more government money, and no more regulations that protect their market. Not to mention that many of them do not even have a real market and solely exist as government contractors.

Then there would be ~$4 TRILLION more dollars being saved, spent, and used as market forces drive them, not as a few men in Washington drive them.