So stovepipe jams don't alway lead to double feeds?
Not always, but it can happen. As you noted in your original post the slide will have started stripping the next cartridge from the magazine to feed into the chamber. Depending on how far this cartridge is fed into the chamber when you tap/rack then the slide may attempt to strip the next cartridge (the one immediately below it) from the magazine and chamber it. This is when the doublefeed occurs.
Is the basic tap and rack a good way to clear a stovepipe jam?
I suggest you avoid diagnosing any stoppage you encounter to determine what particular procedure is needed to clear any particular "jam". This not only slows you down but you may misdiagnose the problem and use the incorrect procedure.
Whenever your gun doesn't shoot when you press the trigger you should immediately tap, roll & rack. Just do it. Don't stop and inspect the gun to determine what the problem is.
My tap/rack process is a little different. I strike the magazine with the heel of my support hand (Seat), then grasp the slide with my support hand. I then "roll" the pistol to the right to point the ejection port to the ground and simultaneously push forward with my firing hand and pull backward with my support hand. Rolling the pistol allows centrifugal force and gravity to help clear the action. I push/pull energetically as if I'm trying to rip the slide from the frame. My "tap/rack" process is best described as "Seat, Roll & Push/Pull".
After I perform "Seat, Roll & Push/Pull", I then recover and fire again, if necessary. If the gun fails to immediately fire again, then I'm going to either move away from danger, if necessary, or use a different force option. When time and situation permit I'm going to attempt to perform a Combat Reload. If I can't insert the magazine into the pistol then the "empty" magazine is stuck (probably a doublefeed) and I have to lock the slide open, remove it, roll & rack the slide a few times to clear the action, finish my Combat Reload (Seat, Roll & Push/Pull), and drive on.
This non-diagnostic technique can be performed without need to look at the pistol. It can be performed while on the move and in complete darkness. It's quicker than a diagnostic technique because it short circuits your decision-making process (Observe-Orient-Decide-Act (OODA) Loop).
With a diagnostic procedure you first "observe" the problem (the gun didn't fire). Then you "orient" yourself to the situation by examining the gun to determine the cause of the misfire. Then you "decide" what procedure to use to clear the problem. Then you "act" to clear the problem.
With the non-diagnostic procedure you first "observe" the problem (the gun didn't fire) and then immediately "act" to clear it without need to "orient" and "decide".
Tap/rack clears many problems
When tap/rack fails then you immediately attempt to perform a Combat Reload because you're more likely to have emptied your magazine than to have encountered a doublefeed. A Combat Reload will get your gun running quicker if all you have is an empty magazine. If, when you're attempting to perform the Combat Reload, you can't insert the magazine into the magazine well, then the "empty" magazine didn't jettison from the gun when you worked the magazine release. When this happens you immediately act to clear a doublefeed. These progressive "observe/act" steps require little decision-making. They're performed intuitively. They minimize your mental load so your mind is free to "Observe-Orient-Decide-Act" to keep you from being shot/stabbed/beaten.
If you "observe" that your gun didn't fire when you pressed the trigger, then you "act" to immediately perform tap/rack.
If you "observe" that tap/rack failed to get the gun running, then you immediately "act" to perform a Combat Reload.
If you "observe" that you can't insert the magazine, then you "act" to clear a doublefeed.
In a defensive situation you want to keep your attention focused on the "external" danger. Your gun stoppage is an "internal" problem. Using a progressive series of non-diagnostic steps allows you to maintain "external" focus. Whereas a diagnostic procedure draws your attention into the gun, at the expense of your ability to quickly sense and react to an ever-changing dangerous situation.