I know that the effective focal length of the 50mm FX lens is actually 50 x 1.5 = 75mm, because I'm shooting with an APS-C sensor.
Not exactly. Not "incorrect", but you have to understand what it means. The 75mm will not be a useful number on DX. The 50mm lens is NOT 75mm, and there is no actual real thing called effective focal length. It is a purely hypothetical concept. Any lens (at any one zoom) only has one focal length, where it actually focuses light from infinity.
The 50mm lens is always only 50mm, regardless if on a DX or FX sensor. It is 50mm, period. That is why it is marked 50mm. 50mm is the only focal length it has.
Now you might want to compare its field of view to some other lens on some other sensor. And it is true that the smaller cropped size of the DX sensor does reduce its field of view, so that (if with a 50mm lens) its reduced field of view compares to what a 75 mm lens on a 35mm film frame would see (or a FX frame is the same size as 35mm film). But if your lens is marked 50mm, it always remains 50 mm lens on any sensor.
Effective focal length is only about that other lens on that other sensor (35 mm film), only because that other 75 mm lens appears to have the same field of view on 35mm film (or FX is same size) as does the 50 mm lens on the DX sensor. The focal length on the DX sensor is 50 mm. Only that other lens is 75 mm, and if on that other larger sensor, it does have the same field of view as the 50mm on DX. We are speaking of two different lenses and two different sensors.
The point of this is that there are many people that used 35mm film for years or decades. They are very used to exactly what a 50 or 75 mm lens will see and do, on 35 mm film. Their experience just knows.
Todays smaller digital sensors change things (cropped field of view from the smaller sensors). This smaller sensor requires shorter lenses now, to see the "same view width" that larger 35mm film always saw. So their experience no longer just knows (yet) on their new camera. So the point of this "effective focal length" thing is to compare, to tell users familiar with 35 mm film what a certain lens will do on their new cropped sensor. If we say this 50mm lens performs on DX just like we are used to 75 mm performing on 35 mm film (field of view wise), then this has meaning to them, they know what to expect from it. However, if you are not familiar with using 35 mm film, then effective focal length on 35 mm film is not likely a useful concept to you.
The Effective focal length published with lenses for smaller sensors always compares to 35 mm film size (which is same as FX size, called Full Frame). However, we can compare the field of view of any two sensor sizes. For example, imagine 1/2 inch and 2 inch sensors (film maybe). The larger one is 4x larger than the smaller, so the crop factor is 4x, and (with the same lens) the larger one will have a field of view 4x wider than the smaller, and will need an effective focal length 4x longer to see the same reduced field of view as the smaller one. Different sensors can be different shapes (3:2, 4:3, 16:9) so crop factor actually compares diagonal of the frames.
For FX and DX, this ratio is 1.5x.
A similar ratio was always true of different film sizes, but not until FX and DX digital were we able to use the same lens on different size sensors. So this becomes a subject of discussion today.