Linux

while this hasn't been a design goal of x86 for ages.

It has been since P4

As you said yourself, it's not the same thing. Proton can occasionally beat Windows because Vulkan might be more efficient doing certain things compared to DirectX (same with other APIs getting translated to other API calls). This is all way more abstract compared to CPU instruction sets.

If Qualcomm actually managed to somehow accurately (!) run x86 code faster on their ARM hardware compared to native x86 CPUs on the same process node and around the same release date, it would mean they are insanely far ahead (or, depending on how you look at it, Intel/AMD insanely far behind).

And as I said, any efficiency gains in idle won't matter for gaming scenarios, as neither the CPU nor the GPU idle at any point during gameplay.

With all that being said: I think Qualcomm did a great job and ARM on laptops (outside of Apple) might finally be here to stay. But they won't replace x86 laptops anytime soon, and it'll take even longer to make a dent in the PC gaming market because DIY suddenly becomes very relevant. So I don't think ("PC") gaming handhelds should move to ARM anytime soon.

Porting games to a different architecture is normally quite a bit more involved than just recompiling them, especially when architecture-agnostic code wasn't a design goal of the original game code. No, Valve couldn't release all their games natively running on ARM tomorrow, the process would take more time.

But even if Valve were to recompile all their games for ARM, many other studios wouldn't just because a few gaming handhelds would benefit from it. The market share of these devices wouldn't be big enough to justify the cost. Very few of the games that run on Steam Deck are actually native Linux versions, studios just rarely bother porting their games over.

I'm not saying ARM chips can't be faster or otherwise better (more efficient) at running games, but it just doesn't make sense to release an ARM-based handheld intended for "PC" gaming in the current landscape of games.

Apple can comparatively easily force an architecture transition because they control fhe software and hardware. If Apple decides to only sell RISC-V based Macs tomorrow and abandon ARM, developers for the platform would have to release RISC-V builds of their software because at some point nobody could run their software natively anymore because current Macs would be replaced by RISC-V Macs as time passed by. Valve does not control the full hard- and software stack of the PC market so they'd have a very hard time to try and force such a move. If Valve released an ARM-based gaming handheld, other manufacturers would still continue offering x86-based handhelds with newer and newer CPUs (new x86 hardware is still being developed for the foreseeable future) and instead of Valve forcing developers to port their games to native ARM, they'd probably lose market share to these other handhelds as people would naturally buy the device that runs current games best right now.

In a "perfect world" where all games would natively support ARM right now an ARM-based handheld for PC gaming could obviously work. That simply isn't the world we live in right now though. Sure we could ramble on about "if this and that", it's just not the reality.