Example: Should both 60amp breakers be on the same side(lug) or should one be on the left and the other on the right?
You are not understanding the setup of panels. The two phase wires are laced in the breaker slots down each side. One side is not all A and the other is not all B. Each side going down is AB AB AB etc.....

But for the sake of simplicity, we could phase out the use of the phase reference when referring to the phase on single phase 240Vac power.
"Phase wires"? We are discussing single phase panels...![]()
Way back when there existed a two phase system. Where 3 phase has each leg at 120°, the two phase system was at 90°. Technically our 240 V system is single phase, center tapped.