I think you have it backwards.
The traditional idea of the consigliere was an older, semi-retired guy who has largely independent of the boss and weighed in on major matters, looking out for the interests of all family members, etc.
In more recent times the consigliere has often been tight with whoever is running the family and still very much involved in the rackets, even running their own crews and operations.
There's some other great replies, but I am always in awe of the Latter Day George Anastasia/Jerry Capeci (whoever you prefer more Ivy).
To incorporate a military chain of command, I've been under the impression that the Consigliere was a fully active Wiseguy, crew and everything, however with the distinction that he was the man seen to meddle disputes and the one to speak to first before asking the Boss or UB for anything. A procedural thing, and to ensure the Boss is not wasting time dealing with seemingly petty issues, whatever they may.
I assume different Families have differing responsibilities of it is the Consigliere does, and I know it's among some Families that the Consiglier is often the one to succeed the Boss, this I imagine having a lot to do with experience handling the day to day, HR type stuff of the Family.