Enforcement of contracts is always government intervention. It's a regulation of business, forcing people to stick to their word on certain issues, despite obvious economic reasons not to.
Not enforcing some contracts is less intervention, not more.
Not enforcing some contracts is less intervention, not more.
I'm not saying it wouldn't happen, I just don't remember such an ancap society existing in the first place.
Within the context of the U.S.'s current economic/legal system, I think it's more in accordance with common usage to think of the existence of private property and contract law as being the basic substrate on which everything else happens, including more specific government action. For example, to continue with the property analogy, we typically think of eminent domain as a state "taking" property, even in cases where a person's "ownership" of a property depends on the government in the first place (someone owns a deed to land they don't actively reside on or use, but since it's legally recognized as property, the government choosing to build something on it is legally recognized as a taking of property). But point taken that this whole contract/property system is itself created and enforced by the state, not some kind of naturally occurring phenomenon.
This may have been common usage through the 1920s, and it may be common usage for people who wish the New Deal never happened. But even then it would be a stretch. This country's legal history is a lot more nuanced than that. What you articulate is probably best described as a minority vision today.
An alternate, more radical view would be that, since the state had created contract law, property law, etc. in the first place, many New Deal laws weren't even regulations or restrictions on anything, merely the state choosing to withdraw some kinds of legal arrangements that it had previously created. But I don't think any New Deal courts were nearly that radical. They instead agreed that they were regulations or restrictions, but held that those regulations/restrictions were within the government's powers to enact, most often justifying them as within the power the Constitution gives Congress to regulate interstate commerce.