1. Nuts (by standardized and MILSPEC/MS/NAS catalog sizes) are slightly shorter than the bolt diameter. Bolt heads (being universely forged with the bolt shaft) are 82% - 90% the length of their mating nut since they are inherently stronger that a nut - which has cut threads. (As strength requirements increase (the higher the grade of the nut & bolt), the longer the nut usually is.
When a bolt or threaded rod extends through the nut by 1-1/2 to 2 threads, the length from bottom of nut to top of threaded end ends up right at the full diameter of the original threaded shaft.
Remember, you have got to design for the field to assemble, take apart, and re-assemble these fasteners - and the field mechanics and millwrights will not have access to a manual or ASME spec. for them, a conservative and easy-to-remember thumb rule is safer as a design criteria than a chapter and verse in a book they can't find. And don't want to read.
2. Tapped holes are a little different: In a forged or machined part like a turbine cassing or pump or valve, it is very, very likely that many different depths are going to need to be drilled and tapped through - all of the same diameter stud and the same nut and washer. What will differ between these tapped holes is the depth of the metal being drilled into.
For manufactoring and repair, a drilled-through speeds up fabrication: coolant runs through, all holes can be drilled straight through (manually or cnc) and all threads can be tapped right through the metal into "air".
If you specify many different hole depths, each time the chips and coolant need to be vacuumed out, wiped out or soaked out, blown clear, etc. That's hard, slow, and expensive work - and often still leaves residue in the tapped hole. Tapped threads can't get a grip in the bottom of the hole anyway - unlike a through hole where the tap can be run all the way to good threads all the way through. So through holes (hole that are apparently way too long for their purpose, are often cheaper and better than closed-end tapped dirt collectors (er, holes).
So, there needs to be some uniform criteria (thumb rule) that allows for varying depth tapped holes: Hence the requirement that a tapped hole must be engaged at least one full diameter of the stud. Easy to remember, easy to apply and check.
And the one full diameter for tapped holes, as you see above, is compatible in form, fit, and function with the "2 threads past the nut" thumb rule I used above for nuts.