One easy way to see this is that an IC is equivalent to a mod announced uniquely named role that claims on D1. Mafia will not counter-claim that claim, so the role becomes essentially an IC.
So the extra power of the unique name comes from the fact they can decide when to claim, with the added risk that mafia may fake-counter claim later. However, math shows that the added power is not that significant.
Now, I suspect ICs are probably less fun to play than unique named roles given the fact that you don't get to make any decisions about when to claim. Unique names become much more powerful in the mid-late game, so you need to stay alive in order to maximize the power of your role. Also, ICs are a prime NK target so they probably won't survive after N1.
Based on this I suggest
never using ICs in a set-up in favor of uniquely named mod-announced roles
.So for example, instead of a mod announcing the following: "player X is an IC"; mod would announce "There is a town member with a role named ABC in this game".
Spoiler: math
