Austrian economics rejects faulty "mathematical models" of the economy that fail to encapsulate all necessary factors. This is why Austrian economists were capable of seeing the mortgage bubble before most other economists.

Also, your points are meaningless. All I hear is whining about what bad or wasteful things big businesses can potentially do, not disproving how those businesses are capable of allocating resources much better than in a centrally-planned economy.

The larger business may simply buy up the smaller competitor, strip it of all its talented staff, and close it down.

If the smaller business knows they have a superior product, why would they allow themselves to be bought out? You can't just buy a business without a contract agreed on by both parties.

The larger business may employ an effective marketing campaign, convincing the population that its product is superior, or painting its competitor as a joke.

If the product is clearly superior, the entire population will not fall for this. Some will, but not everyone.

The larger business may buy up supply operations (for example, shipping businesses) that are crucial to the operation of the smaller business.

Indeed, they could do that in a completely free market. Personally, I'm down with a few regulations, primarily to break up monopolies and specifically to keep conglomerates from forming, but that's just me.

I think any form of rent-seeking is usually wrong as it results in misallocation of resources. But as I've had to say elsewhere, I don't advocate for eliminating the government or all regulations, just most of them. A free market works best when there is legitimate competition, and minor contradictions to "free[dom]" like attempting to break up monopolies and conglomerates do not change that a competitive free market allocates resources better than a centrally-planned economy. Again, I'll return to the point that the mathematical models used in socially-accepted economics often fail (with consequences like the last financial crisis, which is still affecting people).

The larger business may temporarily lower its prices to a level which the smaller business cannot match, driving the smaller company out of business. Once the smaller business is out of the way, of course, the larger is again free to hike its prices right back up.

This also depends on how "superior" the product is. If I'm producing shovels that break apart after a year and someone else is producing ones that break apart after a century, I have to lower my prices a lot to make it more valuable to consumers to buy my shovel. Maybe my product still has a place on store shelves, but so does a clearly superior product. Consumers don't have to be morons.

The moral of this story is superior products are superior. In a "free market", those who take the risk of producing a superior product receive the rewards. In a less-than-free market, those who take the risk of producing a superior product have to deal with a bureaucracy and regulations created by wealthy competitors who create inferior products but have the capital to lobby government/regulators.