I have also looked in vain for such comparative categorization and, though there is consensus of the significant differences between rainfall characteristics (e.g. frontal, convection, orographic) and where on the globe events take place, comparative assessments are far between. There is one here, though (let me know should you want the complete article).
A study on Rainfall Erosivity in Europe (2015) uses a revised USLE (i.e. RUSLE) to estimate erosivity based on rainfall amount and intensity (multiplying kinetic energy by the maximum rainfall intensity during a 30 min period for each rainstorm). Thus, rainfall intensity rates are a crucial element but are not specifically shown in the report. However, the report clearly states that there is large amount of data available regarding rainfall intensity. Given its large geographical scope and availability of data this study may provide interesting ideas for how to go about organizing and presenting WF data.
Other sources are using categories for the intensity levels but often fail to include proper references to their origin – for instance, your 2nd link from AMS contains no reference, Wikipedia (2nd and 3rd categories refer to AMS), and Central Weather Bureau in Taiwan (also no reference).
A simple way of doing categories may be to establish these as intensity levels where, for instance, rainfall rates representing 90 – 100% of highest values correspond to Extreme events, and so forth. However, I wonder what researches and meteorologist would respond to such a system and what they would suggest as appropriate percentage levels.
One impact of climate change often reported (e.g. this search) is the general expectation that rainfall rates will increase over time (i.e. warmer air contains more moisture). The above categories would not capture this dynamic, if only using the percentage system mentioned. Actual rainfall rates remain important (mm/inches per time unit) together with their processed averages (min, high, max) which would change over time.
Climate change hazards are not only increased rainfall rates causing (flash) floods and landslides, but also strong winds of increased strength. It’s interesting that Weather Underground (WU) group our data for wind in three groups (average, high and gusts), which I find very useful.
A couple of years ago, and thanks to a PWS available through WU, I looked at nearly 7 years of wind data, which is clearly too short for any major conclusions to be made. Nevertheless, in that period we did experience a marked increase in both average, high and gusty winds. Significantly, since 2015 many events of wind gusts were above 60 km/h which is when tree crowns start breaking up and trees will fall, which is - indeed - what happened when Nate was still a storm moving north in the Caribbean.
Obviously, both rainfall and wind data are important indicators documenting the unfolding of climate change around the planet. As a citizen science project, the WF network, and – as you rightly say, students, may contribute to documenting such changes. In that context, the rainfall erosivity study in Europe may give some inspirations.
A (global) citizen science project may also turn out to be an important motivator for the community of WF station holders if synthesized data on emerging results is provided as feedback. Indeed, visualizing such data would be a marvelous addition to the GaryFunk map on the location of WF stations.