I've heard GoboLinux [0] does not follow Filesystem Hierarchy Standard.

[0] https://en.wikipedia.org/wiki/GoboLinux

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What you describe is like installing in $HOME. It's not unusual - python virtualenv, ruby rbenv, node_modules. This comes with trade off - either system knows where to search or one has to define per project. By FHS entire Linux tree is a project. In Windows... configuration is pain.

Flatpak someday.

Now, as I think about it, ruby is not like FHS

    └── gems
        ├── irb-1.2.3
        │   ├── exe
        │   │   └── irb
        │   └── lib
        │       ├── irb
        │       └── irb.rb
        └── rack-2.2.2
            ├── bin
            │   └── rackup
            └── lib
                ├── rack
                └── rack.rb
    

vs

    ├── bin
    │   ├── irb
    │   └── rackup
    └── ruby
        ├── irb
        ├── irb.rb
        ├── rack
        └── rack.rb
    

FHS approach does not support multiple versions, gems approach requires declaring version in code or Gemfile, playing with PATH, considerable slowdown https://github.com/Shopify/bootsnap