It is difficult for me to gauge if your reply was meant only as snappy rhetoric, or if you really want me to answer why. The objective of my question was to see if you, or anyone, had found some thinner headers, to save myself some effort, regardless of the reasons.
I have not done research on these DIP sockets to see how much deflection they can tolerate and not degrade their spring force. There was a comment in one of the threads that using a square header into a DIP socket is 'way too much deflection'. Not having looked into this, the simplest approach for me is to use headers of thickness similar to the intended use of the keyboard DIP socket. DIP sockets normally anticipate a rod thickness of 0.25 mm. So, if I am using a header of that thickness, I don't have to bother my mind and think any further. Thus, I posted the question.
The thinner machine pins are about 0.50 mm, which is twice the anticipated typical use characteristic of the DIP socket. Some machine pins are thicker, at about 0.62 mm, and square headers are 0.66 mm. Well, someone previously commented that 0.66 mm will deform the spring.
Another characteristic which crossed my mind are that machine pins are round, while DIP sockets are squared. Inserting a round rod into a square, or parallel planer socket will reduce the surface contact area.
It is for these two reasons, that is, rod thickness, and contact geometry, that I have asked if you had sourced thinner headers. The use of 0.5 mm headers may be just fine for you and anyone else, but since I was putting together a digikey order, why don't I look for some thinner ones and of the correct mating geometry. I remember I have some Arduino headers from about 15 years ago; I just measured them and they are 0.38 mm and flat-planar. If I can find them on digikey, I'll order them.
Plan your life wisely, you'll be dead before you know it.