They may seem common and all, but... However, most peaches in the store aren't all that good. A lot of them are, however, depends on the season and what variety it is. At least it's possible to get a good peach at the store, as opposed to apricots.
But flat out--Peaches are one of the great dessert fruits of the world. They were thought of as luxuries on par with other very high quality dessert fruit like lychees, etc, in a way that figs have never been. A good peach has a strength of character that only the very best figs can match, and the best peaches are up there with the best mangos, pineapples, cherimoyas, etc.
That's why I think that it's pretty ludicrous to want a peach flavored fig. I can understand peach tones making a fig more pleasant, but figs simply can't match anything like what a peach is like, taste and aroma-wise.
On the other hand, peaches are a great deal of trouble to grow and fruit if you're not in California. Here in Georgia and South Carolina, they require a serious pesticide and disease spraying regimen. Figs don't need any of that kind of care. I suspect you'd be better off with persimmons than peaches, depending on how much care and time you want to devote to your tree.