For most aircraft types the maximum load experienced by the tyre occurs during the takeoff roll rather than on landing. In fact it is the combination of sustained load and high rolling speed that occurs on takeoff that is usually the critical design case for the tyre.
As well as braking, heat is generated within the tyre itself during rolling under load, which can result in significant heat build-up in the carcass during a long taxi roll.
Some useful reading matter can be found here:
Goodyear tyre care & maintenance manual
(See in particular the section 'Effects of Operating Conditions')