Edit: OA advocates have won pretty much everything we wanted, there's not much left to be outraged over.
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.
In the end the details do not really matter, it is still absurd that a high percentage of the money paid in whatever way is just profit for company investors, for a system in which 80% of the skilled work is done for fee by the scientists.
I'm not sure if APCs will reduce the paper flood. Especially if the APCs are near the real cost of publishing, having a published paper will always be worth more to the authors. This is how we get all the junk journals that publish anything as long as you pay after all.