I think you are missing the forest for the trees in the middle part of your analysis.
While it's true that Shops has a (growing) number of restricted lock parts, a Shops deck is unlikely to mulligan more aggressively (relative to other strategies) to find them, simply because modern Shops decks rely on cumulative pressure (both lock parts and damage) more than a single tactic to hold an opponent at bay, like it could do in the days of unrestricted Trinisphere.
Similarly, PO is not going to want to mulligan any more aggressively (relative to other strategies) to find the titular card. PO requires a density of mana rocks and other perms to make PO payoff. Thus, it needs a larger starting hand in general.
The point of my post is that this dynamic potentially changes with the rule change. These decks can now potentially function as hybrids where "mulligan to restricted or broken cards (X,Y,Z)" is a much more viable plan B. You no longer have to keep a medium 6-7 on PO because you were a critical mass deck as now you can reasonably hope to mise a Timetwister, Tinker, Ancestral, or whatever. It's less true for Shops but I actually think that PO is a huge beneficiary of the new rule.