The spatial data structure literature is quite incomplete, and there is a lot of confusion about what to use when. Many of the issues with spatial indexing performance at companies I go into is that they are doing it wrong, not that they necessarily have a fundamental problem.

It should be pointed out that R-family data structures should only be used for data sets that are (1) small and (2) relatively static. They scale very poorly in a number of ways. The primary reason they are used in databases is that they can handle interval (i.e. non-point) spatial data types without the possibility of pathological space complexity (bad when talking about databases) and fit B-tree indexing models adequately, which that software understands.

Quad-tree variants can scale well for point data types but are often terrible for indexing non-point data types due to pathological space complexity.

Grid-file variants are the canonical structure for large-scale spatial data sets if the data is static. However, the number of companies implementing these correctly at scale is approximately zero in my experience.

For general, scalable, online/dynamic spatial indexing structures, there is another family of algorithms and data structures (adaptive spatial sieves) that are basically ignored in the literature even though they were first described in 1990, albeit in a not very useful form at the time. If you are doing petabyte-scale real-time indexing of polygons at extremely high rates, this is what you would use but little is published about them because most modern variants did not come out of academia.

And the most advanced algorithm family for indexing point-like data is not in the literature at all.

(Background: my day job involves extreme-scale, high-performance spatial indexing software and I invented a few spatial indexing algorithms back in the day that are still the state-of-the-art in their respective algorithm families.)