How to add an alpha channel to a video? (Sounds simple, doesn't it, but Adobe couldn't answer this.)

Set Matte uses the values of the Luminance, Red, Green, Blue, and other channels to create an alpha channel. If your image has areas that have a value of .5 in the red channel, then the alpha channel will be .5, and that makes the transparency of the layer where the red is at .5 50%.

Color values are always 0 to 1 because they are calculated in float (32-bit). If you check the Info Panel and it is set to 8-bit, you will see values from 0 to 255, but if you extract the data or type in a value in a color property, you'll get 0 (no color) to 1 (fully saturated) for each of the RGBA values. 

Set matte effectively turns any of the available channels into transparency. It works perfectly. You can modify the opacity by putting a color control above Set Matte, like Curves, so that you can adjust the look.

The one thing that Set Matte cannot do, that a keyer like Keylight can do, is combine colors to create transparency. You cannot create a matte from a blue background, like a sky, that may have red and green mixed in. Check this recording and note the Info Panel. Pay attention to the transparency (alpha channel values in the Info Panel.

The only part of that image that will be 100% opaque or completely transparent is the part of the image with pixels that have a blue value of 0 or 1.

I am not sure what you are trying to do, but if you want to use red, green, or blue, or even luminance to create transparency that matches those channel values, Set Matte is the tool you want to use. 

Set Matte will allow you to create an alpha channel from any layer's Red, Green, Blue, Luminance, Hue, Lightness, or Saturation. You can throw in some color correction using anything from basic controls to Lumetri's numerous controls to create an alpha channel.

Did you shoot the footage on the green or the blue screen background? If so, you do the keying. If not, you convert it to a monotone (greyscale) movie  to use it as a keying plate.  You apply for Effect menu > Channel > Set Channels. You find Set Alpha To Source 4's in the menu and set the greyscale movie as an alpha. This way may work well.