Industrial tires are really only good on hard, flat surfaces. The only reason they are used on 90% of CUT's is to reduce turf damage.
I have heard people mention this before, but don't believe that is the true reason. Yes, R4s will damage turf less than R1s, but almost any type of tire will damage turf less than an R1, so that is not saying much! My Kubota with R4s will make a mess of my lawn compared to my Deere with turfs, so I don't consider the R4 much benefit at all.
Many tractor owners don't care about turf, so they would be picking R4s for another reason, likely for front loader work and durability. If the tractor has a front loader that is to be heavily used on mixed surfaces, the R4 is the logical choice. Most types of construction equipment use an R4 tire, and they do it because of the load capacity and thick/heavy tread. Turf damage is rarely ever a factor with construction equipment, in fact I bet the topic almost never comes up. People who know why they would want an R4 tire on a compact tractor would be choosing them for the same reason.
All the tires have priorities and are a compromise at off-design conditions. Pick the one that makes the most sense and know it will have downsides. The basic priorities are:
R1: traction in soil and mud, best for ground engaging work
R4: highest load capacity and damage/puncture resistance, best for front loader work or construction/similar usage
Turf: minimal damage to turf, best for mowing work on lawns