[regularfry]

This has to be the core of it. If the underlying question is "was this alignment intentional" then you could start by asking whether there are extant maps with better cathedral alignment than Mercator.

These places are old. Skellig Michael goes back past 823AD, Mont-Saint-Michel is about the same sort of age, and the Sanctuary of Monte Sant'Angelo goes back to 490AD(ish). San Michele Arcangelo is on top of a pre-Christian pagan temple. Stella Maris is on an Old Testament Biblical site. None of them is less than a thousand years old.

The bar for finding a map that happens to align, and then explaining how it was made, is not a low one.

There is a projection that might fit, though: Plate Carrée is definitely old enough, and a brief visual sanity check doesn't make it look totally off.

[smeej]

Why do we need to assume widespread maps for this? Or even maps of the entire globe? A regional map showing barely more than a rectangle with this as its diagonal would be sufficient to get the point across to the average layperson.

Virtually everything in church design is meant to communicate truths of the faith to illiterate laypeople. That's part of why pictures feature so prominently. They're telling stories to people who can't read. The sense of space, and the drawing of the attention upward, they're also communicating to people on purpose.

If the argument is that the sites were not intentionally built in a line, that it just happened this way, that there just happen to be seven prominent hills with churches built on them that refer to St. Michael (or 6 and Mt. Carmel, which is associated with him in another way), I guess that's a different conversation, but I thought the idea here was that these were lined up somehow on purpose, at least for the latter built ones, and were intentionally built to be "in a line" by some meaning of the term.

[regularfry]

The line is long enough for the curvature of the earth, and the subsequent distortion in the map projection, to be relevant. Notice that they're closer to a straight line on Mercator than to the geodesic: that means if you were to use purely local referencing to align the sites, they wouldn't end up where they are. You only get them to line up when you distort the natural geography with a projection of some sort, so if you want to make an argument that they were intentionally built on a line, you also have to account for the systematic deviation from the geodesic. And that prompts the question of whether that's remotely feasible given what we know of the history of cartography.

What I'd want to know is how old the story of St Michael's Sword actually is. Not the churches, but what's the earliest reference to them being in a line. My bet is that it's well after Mercator, and probably safely after the 18th century, when chunks of Europe got geodetic surveys done.