Are special snowflakes supposed to a good thing or a bad thing?? As for the Joe schmo comment, Ramza Beoulve of Final Fantasy tactics is the probably the best example of a "regular character", as regular of a hero one can get within the confines of a fantasy game. While his Dark Knight and Holy Knight companions are using miraculous magical sword attacks to destroy their enemies, Ramza has only his base skillset (which is just a moderately upgraded version of the generic squire skillset) to wok with.
In all honesty I think having an average protagonist can work, but really it depends on what the game's definition of "average" is. In Tactics it was quite commonplace to hurl fireballs at people, summons magical eidolons into crushing your enemies, and even distorting time by warping across the battlefield. You would gain companions like Agrias, and Meliadoul who have sensational sword powers that make Ramza look like a nobody then you have Orlandu who makes everyone look like a nobody. In the end it was rewarding to face the final boss with a level 50+ Ramza armed with dual wielding Knight Swords, Blade Grasp reaction, Maintenance, and Teleport abilities because as a supposedly "ordinary" character in Ivalice he made it work with whatever average (meaning not NPC jobs like Assassin or Holy Knight) job classes were available.
What I'm trying to say is that you could argue that the Warden and Hawke are "average" PCs (aside from the titles and prestige) they both could have very easily just ignored their priorities (read destinies) and taken the "Reaver" (of Fable) route and did whatever they deemed most profitable while sitting back and watching the ensuing chaos. I mean really Riordin could have been the one to end the blight had he not been captured or died in the end, really there was no special birthright or prophecy stating that only the warden-commander can do this, it is just implied since it is the main character/hero of the tale and is your avatar.