Argument #1: Transitional Fossils

[Heywood]

The problem with Heywood's description is punctuated equilibrium is probably mostly not punctured by spectacular mutations that allows the mutant to ascend the existing wall of the valley, as Heywood suggests. Rather, it is likely mostly punctuated by a whole sale reshaping the topology - ie the ecological environment that has been stable for a long time, and to which existing species have stably adapted, suddenly changed. The walls of the valley may have come down the the floor the valley may have risen up, as it were, and the changed ecology then drove the long stable species to either adapt or perish. They comfortable valley no longer exists, or suddenly merged with other valleys, or had new tributaries valleys suddenly form.

What you describes does indeed happen. The landscape does change over time and that does open up new pathways for evolution to take.

Keep in mind however there is no reason to think that the utility of mutations is constant. Some mutations are more beneficial than others just like some mutations are more harmful than others. If you could quantify the utility of beneficial mutations I suspect you would find most fall in a given range but occasionally an outlier or super mutation comes along whose utility is well outside the normal range. Such super mutations could be so beneficial that they quickly spread through the entire population and lift it out of punctuated equilibrium.