If the GS is 120kts, at 1,000fpm you're not far off a 5deg GS - not what most would call stable, unless it's an approach into LCY. At 160kts, it's just over 3.5degs, on the edge of one red three whites territory.
I think that's the point. If you fly at 1000 fpm down to the runway, say for the last 1000 feet or so, at typical approach speeds that equals an approach angle much higher than the normal 3 degrees.
There are some runways in the world where the approach slope is higher than 3 degrees, and that is then called a "steep approach", is specially mentioned on the approach charts and requires special procedures (e.g. a different flap setting than a normal 3 degrees approach), briefings, and sometimes even special training for pilots.
Now just because you fly such kind of approach unplanned, does it make that so much easier that you can skip all those special procedures required for a steep approach?