The problem with this very accurate method, is that it does not work on many (most?) factory rifles. On custom actions and blueprinted actions sure. But many/most factory rifles require resistance to close the bolt on an empty chamber. Some require significant force to close the bolt, the bolts certainly don't just "fall" closed via gravity alone. You'll never be able to feel the difference between 2 thou vs zero headspace.
I see this bump method referenced often, but it does not apply to many/most of the guys asking the question.
Before there were "bump" gauges this was the methodology used and it worked quite well with factory rifles. The key is removing the firing pin assembly so you can better assess the degree of resistance in chambering the case. You also will be able to tell immediately, qualitatively, if you sized enough or too much. This why you see this "bump" [measurement] method referenced often especially by old timers like me.

However, I'm not advocating replacing the use of modern bump gauges and measuring bump. I'm just saying that checking in the rifle is an effective way to verify that your measuring and sizing is adequate.
When the firing pin assembly is removed, at least on my factory rifles, there is no or very little resistance to the bolt locking and unlocking. You can easily and accurately feel the amount of resistance the case encounters when chambering.
It takes some experience and technique to precisely and consistently measure shoulder bump. Because of inexperience and operator error in precisely and consistently measuring shoulder bump, just blindly using a certain shoulder bump without verify the adequacy of the case chambering can result in cases either oversized or undersized.
I agree that you will not be able to feel the difference between 2 thousandths bump and zero headspace, but you don't have to. As long as the case chambers without excessive resistance, that's enough sizing. There is nothing at all wrong with zero case headspace as long as the case chambers without excessive resistance - this is what a neck sizing die does - it does not size the body or bump the shoulder. Often, you can get several reloads on a case without FL, just neck sizing.
The advantage to FL even with zero headspace is that the radial dimension of the case is also sized which significantly assist in adequate chambering. This is why I prefer FL sizing over neck sizing. While the .001 to .002" shoulder bump is an effective rule of thumb and works most of the time, you should only size enough to permit the case to chamber adequately. I believe it's always a good idea to spot check, in the rifle, to verify that the sizing used results in adequate case chambering. I mean, that's the ultimate purpose, isn't it?