You're missing the context here. PvP vs PvE are terms only defined well in an MMO context (where the Environment is all the computer/AI controlled stuff and Players are...well...players). In that context, when PvP balance affects PvE is when raiders skills are modified to maintain competitive balance in PvP. Since the two styles are separate enough to attract almost a completely separate set of core players...this causes angst. This is where RPS-type balance happens in MMOs. Modern MMOs have completely separated the skill-sets--skill X does one thing against an NPC, but has a much lesser effect (or sometimes a completely different effect) against a PC. NPCs usually don't have RPS-type balancing mechanisms, while PCs often do.
PCs and NPCs play contrasting, yet complementary roles in the game environment. What works for one role fails for another--they have different purposes, needs, and balance points. For example, enemy NPCs are
supposed to die in much greater numbers (in D&D anyway) than are PCs. If a party faces 4 average threats per day, with a 5% TPK chance per fight, they have only an 81% chance of surviving a single day, 66% chance of surviving 2 days, and it only gets worse from there. At an even balance (50% TPK chance), they have a 6% chance of surviving a single day, and a 3 x 10^(-9) chance of surviving a week (28 combats).
This necessitates completely separate build priorities, especially combined with the (true) fact that rolling big numbers is fun for many players. Consider the possible combinations in the simple case of combat. The relevant metrics are the ratios X_NPC = DMG (NPC) / HP (PC) and X_PC = DMG (PC) / HP (NPC):
|
X_NPC high |
X_NPC low |
X_PC high |
Rocket-tag |
"Heroics" |
X_PC low |
Meat-grinder |
Padded-sumo |
Rocket-tag ensues if both ratios are high--if a single hit is enough to kill a character, then the first mover has a tremendous advantage. This is 3.5's default setting at higher optimization levels. By contrast, if you're not the first mover, you're unlikely to be able to participate meaningfully. The entire battle can come and go before your initiative came up. This encourages an optimization arms race, both between party members and against the DM. Retreat is fundamentally impossible--it's nova or die. And nothing is more boring than dying/being completely shut out of the fight right out the gate in a combat that takes an hour of real-time.
Heroics is what happens if PCs can easily (2 or three rounds) kill any reasonable NPC, but the NPCs are less able to kill the PCs (especially with burst damage). This has both good cases and bad cases--in the bad case, everything's a cakewalk and there's no threat. In the good case, the numbers are such that most of the threat comes through attrition, rather than burst threats. You have several rounds (or more likely), several combats to realize you're in trouble and change strategies (or retreat). This is 5e's default setting. Note that this requires breaking PC/NPC transparency as it's inherently asymmetric.
Meat-grinder combat happens when the NPCs can easily kill PCs, but the PCs can't so easily kill NPCs. Low-level pre-3e editions come to mind here. This is a viable game type, but requires a completely different attitude toward things (and a different balancing strategy). Another example is Call of Cthulhu--combat is usually a bad idea there, especially with eldritch monstrosities. This also requires breaking PC/NPC transparency (or at least changing the relationship between "CR" and APL).
Padded-sumo combat is the trap that high-level 4e play fell into before they redesigned the monster-creation formulas to push the NPCs damage up and drop their health a bit. Fights take forever and are low-lethality (for anyone). Boredom often ensues. This one is compatible with PC/NPC transparency, but doesn't require it.
Depending on what kind of game you're going for, any of them (except maybe padded-sumo) are viable. But they produce very different balancing strategies.
Spoiler: NPC/PC Transparency
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In 5e, PCs use a certain set of rules for character creation, designed for their role as the central characters of the narrative. NPCs use a separate set of building rules (more like guidelines) for their role as the foils, the stage dressing that the players interact with. This helps in quickly standing up a set of NPCs and give them the important characteristics for the part where they directly and mechanically interact with the PCs (combat and social encounters), while leaving it open so that you can have, for example, a master magic-item craftsman who isn't an accomplished adventurer with a bunch of HD that can take on whole armies by himself. Or an accomplished farmer who is just as weak and frail as any other commoner in combat (1 HD, no combat proficiency). Or any other of a host of normal people the PCs might meet. Since you can give NPCs whatever abilities make sense (without having to muck around with class levels, skill points, feats, or whatever), you can have people with all sorts of fantastic abilities that are explicitly not spells, nor are the users spell casters. You can have a dedicated temple cleric who can pray for a miracle, but can't cast a spell normally. Or populate a world without having to carefully balance the numbers of each level of spell-caster to avoid breaking the setting wide open. It's also WAY faster to build and run monsters on the fly--you're not carrying around the baggage of a host of levels, feats, and skill interactions.
I think a difference here is that, for me, the rules are simply a UI. They're not the underlying fictional reality. They're just a way of simplifying that reality in a way that is suitable for a game. The rules only govern the interactions between PCs and the rest of the (DM-controlled) world. You can't use social skills on other PCs; you can't assume that the spells in the books are the only ones in the world or that they're really as standard as the books make them seem. In the fiction, fireball doesn't have a nicely spherical explosion with a fixed, nicely-rounded maximum range. That's entirely an abstraction made to make the game playable. It tells very little of the exact details of what's going on in-game. Same with classes, levels, HP, ability scores, etc. Behind the scenes, the NPCs use whatever rules are needed to make an engaging setting that's fun to play in. Nothing more, nothing less.
Now, of course, other games are designed around PC/PC conflicts. This necessarily requires other design assumptions that are incompatible with the "team vs world" model of D&D. And that's fine. Just don't try to import one into the other (or vice versa).