You've decided that it has to be the traditional distro package manager providing the solution - but that isn't going to happen, because those have been designed to manage a single installation of interdependent software with no distinction made between core system libraries or services and end-user applications. The solutions to the problems that come from that - which also make it extremely simple to fix issues like the one you have using a single config file - led to the development of Flatpak and Snap.

Some traditional mutable distros also ship with Flatpak + Flathub configured out of box and present them alongside and with equal importance to their own distro-specific packages - e.g. Linux Mint, PopOS, Clear Linux, CentOS, and Fedora Workstation. And Ubuntu is pushing Snap. So they're all unlikely to start putting work into enhancing their distro package managers to start providing the desktop software specific features that you want.

Yeah, packages for things like Blender and Steam do exist in most distro repositories. But they make no distinction between packages that provide software like that and packages that provide core OS services + userland (systemd, pipewire, coreutils, cups, a desktop environment, and so on). What you want requires a distinction between those things.

See SteamOS, Fedora Silverblue/Kinoite + universal-blue, openSUSE Aeon/Kalpa, Endless OS, and possibly in future Ubuntu Core Desktop as examples of modern systems (or systems in development) that make use of traditional packages as the building blocks of the base OS, and then lean on application distribution methods like Flatpak or Snap to provide desktop software. Use of the distro package manager for software like Blender is explicitly discouraged by all of these.

Distro specific fixes and configurations shouldn't be necessary as long as the OS provides what the application platform needs (desktop portals, audio server, display server, print server, message bus, etc) Flatpak doesn't even prevent distro specific repositories if it's really necessary either; Fedora ships with their own Flatpak repository in addition to Flathub.

You want better control of or isolated and relocatable end-user software installation, and it already exists - it's just not being done at the traditional package manager level, and I haven't heard about any development effort going towards changing that.

The package managers and official repos for most distros would be better thought of as lego blocks to build an OS from - they have no concept of OS and application separation, and splitting installation of an OS across multiple physical drives doesn't really make sense.

Application focused distribution methods with a clear separation from the OS like Flatpak or AppImage do support this.

AppImage - drag the .appimage wherever you want it.
Flatpak - supports system and per user installs (under home directory) by default. Additional installation directories can be configured, but I'm not sure if any of the GUIs expose this feature - so likely doesn't currently pass your bar of not needing to use the command line at all.

You might have just had bad timing - the release notes for Proton 8.0-4 mention

Fixed EA Desktop having a blank log-in window after its recent update.

It's currently a test release so should be out shortly, but if you want to use it immediately there's some info on enabling it early at https://www.gamingonlinux.com/2023/09/proton-80-4-is-now-in-testing-with-a-release-candidate/

I don't find the Steam Deck unwieldy. It is big, but the design and weight distribution makes it comfortable to hold - I don't even think about it when I get into a game on it. For comparison, I find the Switch Pro controllers very slightly smaller than I would prefer, but comfortable too, and the DualSense to be about right.

Steam Deck doesn't currently support being the streaming host (at least, SteamOS currently doesn't - but I wouldn't recommend wiping that as it's one of the best parts of the deck).