Anarchism is typically distinguished from and is distinguishable from (other forms of) libertarianism — to make arguments against anarchism while saying they’re against libertarianism is kind of like making arguments against the U.S.’s policy of “extraordinary rendition” while saying it’s an argument against foreign policy.

The non-anarchist libertarians, which are most of them (e.g. minarchists, conservative libertarians, etc.) all think that the government should enforce contracts, and anyone seriously advocating for that position will have some story about how government is funded (for instance, government services will be purchased for a fee).

So your characterizations before were simply wrong.

Libertarianism has serious issues — in this response you touched on some of them. But that doesn’t mean that all your criticisms are valid. It’s entirely possible to make invalid arguments against wrong things. For instance, murder is wrong, but “murder is wrong because all the dead bodies will turn the oceans into toxic sludge causing a mass extinction” is not a good argument against murder. It’s nonsense.

So, to review

1. Libertarians mostly believe in contracts; those who don’t are more properly called “anarchists”
2. Libertarians have ways to fund government; they don’t expect it for free.
3. Therefore, your arguments against libertarianism were poor arguments.
4. That you made poor arguments does not mean that good arguments do not exist, or that libertarianism is a great idea. It just means that you need to work on your arguments.