The living room is an area. It's an area known as the living room. But a living room cannot be a living-room area.
"Living-room area" would make perfect sense in a reference to an area being used as a living room in a dwelling that doesn't have rooms as such -- a loft, or perhaps an RV. "Living-room area" would make perfect sense in a reference in a reference to the living room and some adjacent real estate. But if you mean "living room," say "living room."
The D.C. area is an area known as Washington, D.C., or just D.C. But Washington, D.C., cannot be the D.C. area.
"D.C. area" makes perfect sense in a reference to Washington and the adjacent region. But if you mean Washington, D.C., say "Washington, D.C."
A break point is an opportunity. But a break point cannot be a break-point opportunity.
Insofar as a break point could be called a break opportunity (you win this point and you break serve, meaning you win a game when you're not serving), "break-point opportunity" could be viewed not as redundant, but as a way of saying "opportunity to get to a break point." At 30-40 the receiver is at break point, with a break opportunity, so then perhaps at love-30 or 15-30 or 30-all the receiver has a break-point opportunity.
To review: If redundancy and wordiness don't bother you all that much, go ahead and say "living-room area" when you mean living room. But "break-point opportunity" is ambiguous. Even if you scoff at "Omit needless words" (as I sometimes do), there's a word there that is begging to be omitted.