My applications (forest and field) really call for ag tires. However I must drive my tractor across the lawn from time to time, and for that reason I have R4's. There's no way turf tires would work for me.
The R4's are a compromise, short of two tractors I'm not sure I had any viable alternatives. The R4's _will_ rip my lawn, I have to be careful. Dry lawn if possible. 2WD only. Drive "gently". Even with all that, the weight of the tractor (say 6300lbs with lighter attachments) is probably compressing the heck out of the roots, but this is my first season and we're still coming off winter, so it'll be a year before I really know how that plays out, and the weight factor probably isn't much helped with turf tires.