If I recall correctly, the body of work that resulted in MTD guidelines for branch connections originated following a large number of failures in duplex stainless, which was a newish material offshore at the time.

Failures were mostly at the header weld toe, where it was thought excessive weld heat or mass caused localised hardening. Systems were commonly seawater, which due to DSS properties were run at higher velocities and in smaller diameters than other materials, and consequently were at risk of flow / turbulance induced vibration. I believe that comparisons with reinforced and simple stub-in branch connections showed lesser problems therein.

I personally doubt that there is much more than an risk / economic decision to limit bracing to 600# and above. However as pointed out already, branch valve mass increases significantly with pressure, so does header wall thickness and consequently stiffness and this may also be a contributory factor in development of excessive local stress.

There is a strong argument for bracing all free standing small bore connections ... for higher pressures, reasons as above and lower pressures to add mechanical strength, if for no other reason than protection from that 240lb hairy ar$ed fitter climbing up the pipe rack.