In Kansas City, places will sell out of the point because that's why you make burnt ends with. Yes I'd say it's the fatty piece of the brisket.
Leave your brisket whole, take it out when the flat hits 195 and passes the "prod" test. Take it out and cut off the point (it's roughly in a U shape) and put it back it for a couple of hours.
Anytime I serve a brisket, the point is the preferred piece by most as with the fat, it has lots of flavor.
If you don't like that part, don't serve it. Or do flats only (but the you'll have different issues).
Ummmmm Burnt Ends (someone else said that)
