Post-mandate, I've been submitting to closed access journals and getting OA on the side for free due to the mandate. Pre-mandate, I only submitted to paid OA journals, and paid ~ $3k each time for it.
The article claims the solution is "every government grant should stipulate that the research it supports can’t be published in a for-profit journal. That’s it! If the public paid for it, it shouldn’t be paywalled." That's an equivocation fallacy. Whether a for-profit journal publishes the work at some point is orthogonal to whether it is available un-paywalled, which it now must be.
You say that publishers replaced subscription fees with APC charges, but I haven't seen this happening when I've submitted papers recently. Journals need new submissions or they lose mindshare. Authors are price-sensitive and will shop around. Starting a new journal isn't that hard (it can been done as a side project) so high margins will likely be undercut. I have no idea why the author chose to pay a $12k APC; they probably didn't need to. Finally, closed-access journals will have residual subscription income from their closed-access archives for many decades; if the author wants to kill that income stream off, their proposed solution will not do it. So while I agree with the article's condemnation of the publishers, who are certainly no friends of science, I think it's wildly off-base on pretty much every other point.
Author-pays APCs are even potentially a good thing as long as they aren't much higher than the cost of publication. Universal APCs would provide some pressure against publishing many low-value papers that aren't really worth the time it takes to read them. The paper spam is kind of getting out of control.