I think in your situation TRAC should have been on... it may have been enough to have helped.
Other than that, everything sounds like it worked as designed.
We have open differentials in the front and rear, you should try applying a little brake to generate some traction, which is what TRAC should have been doing for you if it was on.
Most 4 wheel drive trucks, are still just two wheel drive trucks.
Most 2 wheel drive cars, are just one wheel drive. hence the term, one wheel peel, and peg leg...
People spend big money on lockers as an aftermarket mod, really the only way to get true 4WD.