Perhaps the most controversial of TBN topics.
I have sandy-loam in Florida. I never have mud, nor clay, nor snow, to deal with.
I have had three tractors, each larger, each with 4-WD. My last tractor and current tractor have carried FELs. All three have been shod with R4/Industrial Tires filled only with air.
I try not to compact my soil. The only time I intentionally compact my soil is when I roll in very small seeds with my Cultipacker, in a limited area.
When I need counterbalance, perhaps
25% of engine operating hours, I mount a heavy implement on the Three Point Hitch.
Filling rear tires is good if you have sloped ground to deal with. Filling rear tires lowers the center-of-gravity for the tractor. (But first move rear tires further apart, if possible.)
Filling rear tires may be necessary for adequate traction on tractors with 2-WD, but NEW tractors with 2-WD are a very small category.
A'hm for air.
TBN ARCHIVE:
FILLED VS AIR IN TIRES SITE:TRACTORBYNET.COM - Google Search