To my knowledge there is not an ASME, ISO or other industry standard that embraces thread engagement rule-of-thumb design for minimum thread count.
As I understand design and engineering industry practices the rules of thumb for thread engagements are based on design analysis of actual thread engagement designs. Most correctly, all thread engagement designs should be analyzed for full tensile strength however this is not practical nor required for all design and engineering activity. It is for these reasons that our rules of thumb for minimum thread engagement are used throughout industry. The rules I'm most familiar with is a minimum of 1.5 x Major diameter thread engagement for static loading and 2.0 x major diameter size for dynamic loading.
For your "3 full threads as a rule of thumb," statement - that sounds risky for most any end item based on the variations in manufacturing and assembly
When in doubt - an analysis under worst case loading + a factor of safety is done.
The following is what ASME has to say..
Per. ASME B1-13M, appendix B, page 50
"In general the length of engagement of mating threads is selected to utilize full tensile strength of a bolt prior to shearing and nut threads. Other applications may require internal thread shear prior to failure of theoretically threaded part. ..."