The military studies on barrel life have all concluded heat is THE major factor.
Of course heat is a by-product of pressure, but in rifle cartridges the major factor in heat level is the bore-to-powder ratio.
If pressure were the major factor in barrel erosion a .300 H&H (58,000 psi SAAMI Maximum Average Pressure) barrel would last longer than a .308 (62,000 SAAMO MAP). It doesn't.