Rothbard’s ideal system would be quite different from one everyone is used to. People have grown up in a world where you can sue someone for saying something that embarasses you. You can take someone to court for simply promising to mow your lawn and then not following through on it.
From a logic standpoint, this creates much bigger problems than the ones you say you can probably imagine in a voluntary society. Information is not property. It is not scarce, it cannot be stolen, and it cannot be damaged. Therefore it cannot be owned. To claim you have “a right to your reputation” for example, is to claim you have a right to the thoughts of other people (in this case, what they think about you.) It certainly doesn’t take much to realize the severe flaws in this notion…and the problems that could easily arise not only from a flimsy interpretation, but if this were taken through to logical and even more specific conclusions.
The same goes for promisory contract law…the idea that you should be able to be forced to follow through on a promise…or on the expectations of someone else. Such a system is incredibly dangerous, and certainly is against liberty.
Rothbard goes into this in a later chapter in The Ethics of Liberty…