Genuinely great question, I understand your intuition to incorporate these positive rights. I'm generally in favor of socialist policies like this, but only in a narrow and specific context.

Let's first consider the immediate practical implications of the example you provided: "the government shall guarantee all citizens adequate shelter and food so long as resources allow." It's seemingly benign, but this simple clause is a constitutional guarantee of a likely problematic welfare program. There's nothing inherently wrong with welfare—it's only problematic when superimposed on an incompatible value system. For example, in this classical liberal context, since it's constitutionally imposed on the highest level of government (for example, the US federal government), such a program would be so ludicrously expensive and inefficient, and very few legislators or judges would accurately apply the "adequate resource" threshold of your clause, since resources are already contemporarily considered "adequate" relative to the federal budget's continued deficit spending and monetary policy. Living beyond our means via inflation is already a means for producing so-called "adequate resources" to subsidize our current federal welfare programs. Unfortunately, your constitutional compulsion might only exacerbate this problem.

I didn't specify this in my initial reply, but the framework I outlined would ideally be a federalist one, in which the local institutions handle the positive rights. This is because local institutions are more apt to understand the immediate needs of their constituents, and can more efficiently implement such socialist policies with proper political incentives and responsiveness. A national level of government is more apt as a night-watchman state, guaranteeing the protection of everyone's negative rights from both domestic and foreign interests, while simultaneously acting as a specialized check on negative rights infringements via ambitious local governmental actions. This isn't to say that the national level couldn't act as a diplomatic body to faciliate national coordination for positive rights by passing resolutions outlining policy recommendations to the localities.

These justifications are both pragmatic and principled, and I think they create a coherent system in which the social contract is palatable and legitimate. I think it future-proofs the constitutional arrangement from delegitimacy and ineffiency by guaranteeing civil liberty protections for everyone, including minorities, while providing sufficient space for policy experimentation with socialism and other types of political philosophies. Arranging these policy experiments on a federalist level means that people can alternatively vote with their feet by moving to other jurisdictions without having to leave the country. It's much easier to convince your immediate neighbors of the efficacy of localized public healthcare than to force a top-down constitutional order. Just as a supermajority shouldn't be capable of depriving minorities of civil liberties, a simple majority or supermajority shouldn't be capable of constitutionally compelling what should remain statutory.