@botvinik peacekeeper is an expensive spell at 3 mana, and once in play remains vulnerable to mana denial. there are other cards that likely win the game against shop when combined with stony that are better on their own than peacekeeper is on its own.
I think that, especially in the contest of a back to basics mana base, you are underestimating the guy. It is great versus Hogaak and dredge who typically have at most two ways to remove it in the 75 witch they may not even bring in if your main board shows few or no creatures. Those decks have no way to get to 20 without attacking so the effect frequently completely locks them out. But it’s not only good in the graveyard matchups. Eldrazi tends to board out creature removal for more disruptive elements when you show a creature light or devoid main meaning it can beat them in a single card as well. Without a stony silence it is only a stumbling block vs shops but it can frequently buy enough time to get one online especially if you have the ability to counter the first ballista. Now your point about being venerable to mana disruption is true but I have found great success recently playing more fetch dependent decks that run less duals and more basics and they can be very solid and hard to attack. I have found even with more normal man bases once I get to 3 man it is very hard for shops to drop me to 1 mana. While I will admit 3 mana is a lot peacekeeper is not inherently more expensive and slower than the other grave hate effects. Since they have to stop creatures from entering play and he can stop them once they have already resolved coming down a turn later is not actually any slower to come into effect.
Now I want to be clear I am not making comment directly about your conclusion you may be correct or not, but I think you were much more dismissive of the card than it, deserves wether or not it is ultimately the best option.
Also I cannot think of another card that is so effective versus that spread of decks, doges force of vigor and thorn effects, and does not care about force of negation. If you can name such a card please speak up as I would love to try it out.