As SRE and others have pointed out, fly ash has been used in portland cement concrete for many years. There are several other advantages to using fly ash as well as those mentioned. In particular, it has the potential to reduce alkali-silica (ASR) and alkali-carbonate (ACR) reactions because it reduces the total alkali available for such reactions when substituted for a portion of the portland cement.
Codes recognize this substitution and consider fly ash to be part of the cementitious material in the mix as it does hydrate and impart strength to the concrete, albeit slower in gain as stated. When you read or hear the term water-cement ratio, it is really water-cementitious material ratio which might include fly ash, ground blast furnace slag cement, or other materials having a pozzolanic effect.
With appropriate consideration and fitting to the application, there is no reason fly ash shouldn't be allowed in certain concretes.