It is a National BSA policy that all merit badge counselors register with the local council. This is for the following reasons:
1) to make sure that they undergo the background check, if they are not registered;
2) to ensure that they undergo MB training -- the most important part of which is the reiteration of the "Nothing More -- Nothing Less";
3) to have some sort of self-qualification for the Badges for which one is serving as the MB counselor (simply fill out the form);
4) to assist the council in the development of a current MB counselor list (and to keep it current -- most councils send out an annual form that needs to be completed to keep current as a MB counselor).
There is nothing wrong with completing your annual form or adding a statement on your MB counselor application form that you would like to only be a counselor for XYZ troop.
However, unless you have counselors for all 123 MB, you will have scouts from your troop going outside of the troop MB counselors for assistance. Is that fair if your troop leaders/parents who are MB counselors for MB that scouts in nearby troops need refuse to assist these scouts if your scout are going out of troop for MB?
50 year+ scouter -- have held almost all adult leader positions in Cubs, Scouts, & Venturing, currently serving as Council Scouting for Youth with Disabilities Chair.