I'm not sure calling the rights legal fictions rather than full-on fictions subject to aesthetic rather than just pragmatic evaluation makes much of a difference here.
You say the fictitiousness wouldn't make the applications challengeable as a matter of policy, but that's because the rules would be evoked, like the rules of chess. Once the rules are accepted, when you're playing one game rather than another, some moves become legal and others are prohibited. But the question is whether we should play that game or invent another or modify the rules, given their mere fictitiousness.
If you polled libertarians about whether they think the rights of liberty are made up, do you think the majority would agree? Or would they instead say the rights are objective and are proved by rational demonstration or by divine revelation? I suspect most wouldn't agree that the right to liberty is just a social construct. They would say, for example, that we really do "own" ourselves (in some sense that dissolves upon scrutiny).
The Declaration of Independence says, "all men are created equal" and "are endowed by their Creator with certain unalienable Rights," among which "are Life, Liberty and the pursuit of Happiness." If liberty is fictitious, is the Creator likewise a legal fiction, a noble lie? If so, what else follows from the gamesmanship of social life?
Remind me, was it with you I was speaking some months ago in these comment sections, about game theory?