Cowen has criticized the Great Barrington Declaration at length in public. You can read David Henderson's response here. (For ease, I'll link to part 2, which contains a link to part 1.)
Cowen's strongest argument is that we shouldn't open up or even engage in targeted protection, as the GBD recommends, because the best strategy depends upon anticipating what's coming. Since, he claims, a vaccine and other treatments are just around the corner, it makes sense to stick it out a bit longer and wait for these treatments, rather than pursue a herd immunity strategy in which the young and low-risk get the disease and become immune.
But then, oddly, when you read Marginal Revolution, every other article is about how other countries are effectively pursuing vaccines, but the US is way behind and has institutional structures which will keep it behind. Even today, he has an article about the US has suspended one promising trial even though the obviously-not-reckless British are moving forward.
Cowen says that libertarians should focus on making government behave better. Sure, why not? But isn't there also a point where we should admit that a particular government sucks and is incompetent, and worse, that there is little we can do to induce it to become more competent? Isn't being responsible about admitting how bad your particular government is and how little you can do to change it? (FWIW, Cowen and I live in the same neighborhood. Our neighbors are the government.) If the ship captain is routinely incompetent and drunken, it's fine to point out that he'd be a better captain if he stopped drinking and took some navigation classes. But at some point you'd better realize you can't count on him, period. After all, as Scott Sumner points out, our government almost never picks the low hanging fruit from economics. Or, as I've been pointing out, in a year when BLM is continually on our minds, the better major party candidates are some the architects of the very problem BLM wants to solve. That's how lousy American government is.
Cowen's state capacity libertarianism is a fine ideology for Sweden, Denmark, and maybe even Germany, where leaders are generally competent and open to smart ideas. It seems misplaced in the US, where our leaders are generally incompetent and focused more on posturing than policy.
Indeed, Cowen's own efforts seem to be living proof of that. How much has the Mercatus Center--which tries to make government smarter--paid off? How much has it succeeded in pushing the government to behave more competently? (Note, I'm not saying this to bash Mercatus, which I think does lots of good work.) As far as I know, the only major policy idea that the Mercatus Center sort of funded which was implemented were the lockdowns themselves, though Ferguson would have had that same influence without funding from Cowen. A Straussian reading of Cowen is that he is actually falsifying the theory of state capacity libertarianism.
At any rate, I want to note a generally fallacious way of thinking. People will say something like, "The best response to this crisis is to pursue policies A, B, C, and D all at the same time." For instance, one might recommend lockdowns along with a massive income redistribution to prevent bankruptcy, drug use, suicide, and divorce. It's fine and fun to write in your notebook what package of policies you think would be best. But in the real world, if we aren't going to get that entire package at once, that changes whether you should continue to recommend the other parts of the package. For instance, if there is little or weak evidence we will get a working vaccine in the US in the next six months, then perhaps we should not recommend continued lockdowns, school closings, and the like. If we have weak or low levels of redistribution, we should perhaps not recommend such lockdowns, which very much hurt the poor, uneducated, and young, though don't much hurt rich people like Cowen and me. And so on. Even if a particular package of policy responses (A-D) is optimal, it may be that any proper subset of A-D is disastrous or quite bad.
A proper state capacity libertarianism would often say things like, "Since we're not going to do A-D in combination, perhaps we shouldn't do any of A-D at all."