You could simply plot recommended sizes for clickable items over time.

Windows 9x used 125% text height of 10pt as clickable item height, that's around 0.441mm.

Android 4.0 recommends a clickable item height of 48dp, "roughly one centimeter".

Android 5.0 uses 56dp (1.17cm), and on Phablets and Tablets even 64dp (1.33cm).

For items in lists, a second effect was seen, as it became recommend to show more info earlier, the number of list items visible at the same time was reduced. A multi line list item has a minimum height of 72dp (1.5cm), average is more around 96dp (2cm).

A similar effect can be seen on Windows, in UWP, the average item height also went to almost exactly 1cm in lists or menus.

This all fits well, as the smalest reliably clickable element in a UI is ~1cm on its smallest dimension.

This is also a common issue with HN, where voting buttons are 0.3 by 0.3cm, even on mobile, and as result I misclick ~2/3rds of the time, but no one seems willing to fix this.

I'm not aware of any systematic analysis. However, my expectations are that we would see relatively constant information density until about a decade ago. The simultaneous increase in available pixels and increase in prevalence of touchscreens has made it possible and in some cases desirable to drastically reduce information density without rendering interfaces immediately unusable. The problem is that touchscreen-oriented design is infecting non-touchscreen software.