It does save a purpose. For example in the OP's non-clustering example all of the Britain is covered in dots, I'm talking at the highest zoom level, while the Atlas Obscura version, the one that uses clustering, does a better job of providing data by mentioning how many points that general area contains.
In such cases I generally prefer displaying counts of points in defined areas, rather than using clustering (e.g., when zoomed out, show counts per country, and when zoomed in more show counts for states or equivalent sub-national areas).
If clustering is acceptable the visualization probably shouldn't be a map.
If you have less than hundreds of thousands of points, you can probably get away with drawing individual dots on the map. Computer screens are high res.
It's technically feasible to just draw all the individual dots but it doesn't necessarily convey the information better.
When individual points are drawn close together, they're hard to discern without zooming right in. Even with additive opacity, they max out quite quickly once a couple of dots overlap.
I think that's incorrect. Brains/eyes are good at looking for patterns.
Then, the dots should be less than 100% opacity, which helps convey density wherever they overlap. It's feasible in overpass turbo with its rather simplistic MapCSS, so it should be possible in proper web mapping libraries.
The demo shows exactly that with the density dots, no?