Well, having a caprifig helps ensure that you have wasps to pollinate your figs. People trying to breed Common figs will use one of those persistent caprifigs as the male.
Here in CA, Caprifigs are a "public nuisance" and unless properly maintained are subject to removal by the local ag department. You're supposed to remove the mamme figs, split them open, and treat with a fungicide. The Mamme figs can be treated without hurting the wasps. It's against the law to have Mamme and profichi figs on the tree at the same time. The reason is that the fig wasps tend to spread things along with pollen - often leading to rotten figs.
By law in California, if you're growing Smyrna figs, you may have 1 caprifig per 66 trees.