Unlike a printed page, there is no concern on a screen about text on the other side showing through. There is therefore no possibility that mismatched baselines will reduce the contrast in leading areas between lines as a result.
For a single-column article such as the one we’re discussing here, there is no concern about whether text in adjacent columns may look untidy if the baselines are slightly misaligned. Nor is there any concern that a reader may inadvertently continue reading across columns if baselines do line up and there isn’t a clear enough separation between columns. (However, these might be relevant concerns in other layouts.)
But mostly, by trying to keep to some artificial mathematical pattern, we might actually be making the reader’s experience worse. Spacing between paragraphs usually winds up much wider than it traditionally has been when this kind of strict baseline grid is present. The same goes double for headings being moved further away from the material they introduce. We know human perception is influenced by proximity, and if spacing between related items becomes too great, that connection can start to weaken. That might become an issue here. (If you’re familiar with your browser’s developer tools, you can go ahead and try this for yourself: there are p+p and h2+p rules for this article, which you can vary to see whether you prefer tighter spacing even though it doesn’t follow the baseline grid.)
Despite huge amounts of advocacy, there seems to be little evidence that the kind of strictly uniform baseline grid recommended in this article actually makes anything better. Does it improve readers’ subjective personal reaction to a text? Does it improve objective reading performance in some way? I’d be interested in any relevant research, and very willing to revise my opinions if proper studies say I’m wrong, but sadly in typography hard data is often hard to find.