Posting on this account for credibility? :^)
It is certainly in the interest of the game's health and longevity, specifically for more casual players, to aim for symmetry between PvE and PvP. However, I'd argue that the existence of an Uber tier and the aforementioned symmetry are not mutually exclusive. I feel like an elegant and simple solution is just to raise the difficulty of PvE encounters to suit the strength of what would otherwise be classified as ubers in PvP.
One such way of doing this is by creating PvE encounters that aim to defeat strategies which would be generically powerful. I would turn to Hearthstone's PvE encounters to demonstrate this idea. Many of the PvE encounters in Hearthstone that have been recently have very specific conditions that urge a player to come up with certain strategies to beat the encounter. It is nearly impossible to use a generically powerful PvP deck in these PvE encounters because they have conditions which do not exist in PvP settings (in other words, the AI is cheating). Additionally, some of these PvE encounters have "obvious" solutions, and the designers predicted that by implementing ways to specifically punish those easy solutions, prompting the player to become even more creative.
I think this example is particularly transferable to Pokemon because Hearthstone is a card game which has very similar components and pacing to Pokemon; it is a turn-based game which requires the player to navigate encounters with a predetermined set of tools (deck in Hearthstone, team in Pokemon).
One concern with this approach might be that it doesn't "teach" players PvP, but I would argue that although my suggestion implies the potential introduction of mechanics that do not otherwise exist in PvP interactions, Pokemon PvP is based around a few core concepts that could be emphasized in PvE contexts similarly even with the addition of mechanics or with design choices that specifically target obvious solutions.
Ultimately, PvE interactions are always soluble while PvP interactions are not because PvE is inherently less dynamic than PvP. No matter what, people will always find optimal strategies to defeat PvE interactions, so trying to achieve symmetry with PvE and PvP is pointless. One has a static state while the other is dynamic. However, urging players to come up with new and creative ways of defeating PvE encounters is what makes them exciting and engaging. If a player could use a generically powerful strategy that they derived from PvP, I would argue that it reflects poor design, whether we are talking about ubers or not.