Filling the rear tires is a counterbalance to a Front End Loader, so when you pick up a moderate to heavy load the FEL bucket and load will lift, rather than the rear wheels. However, filled tires to not relieve the strain on the front axle. Ballast on the 3-Pt. does relieve front axle strain.
If you have a 2-WD drive tractor, unusual these days, you may want to fill the rear tires for additional traction when using ground contact implements mounted on the Three Point Hitch.
Dealer installed tire fills should always have an anti-freeze component.
Personally, I prefer to keep an implement on the 3-Pt and NOT load the tires in my part of Florida, where mud is never an issue.