This would open up an incredibly large number of doors for PowerShell

Without a good consensus what is expected from each combination of operator and related (non-primitive) operants, I personally think it will open up an incredibly large number of pitfalls and caveats.

Anyways, the error messages you get from your wishful thinking:

InvalidOperation: Method invocation failed because [System.Management.Automation.PSObject] does not contain a method named 'op_Addition'.

contains the hint to how you my create your prototypes or custom types:

Class MyCustomObject : System.Management.Automation.PSObject {
    static [MyCustomObject]op_Addition([Object]$Object, [Int]$Value) {
        $PSObject = $Object.PSObject.Copy()
        $PSObject.Value = $PSObject.Value + $Value
        return $PSObject
    }
    static [MyCustomObject]op_Subtraction([Object]$Object, [Int]$Value) {
        $PSObject = $Object.PSObject.Copy()
        $PSObject.Value = $PSObject.Value - $Value
        return $PSObject
    }
    MyCustomObject() {}
}

$foo = [MyCustomObject]@{PSTypeName='foo';Value=42}
$foo += 1
$foo.Value # returns 43

$bar = $foo - 5
$bar

Value
-----
   38

I think defining it in a class is a mostly acceptable workaround.

From a performance perspective and a "don't upset the applecart" perspective, this would be acceptable.

From an "easy of use" perspective, I suspect far more people use Add-Member than classes.

Since any individual writing a script or module would be overloading the operators for their own types, I don't believe it would cause catastrophe either way.

Thanks for showing it can be done with classes though!

The Engine WG discussed this issue. We see the value in the concept of allowing ETS to override arithmetic operators, but on its own it's not a feature we think meets the bar for impact at this time. We may consider improvements to ETS in the future that could include this feature in some way.

We are converting this issue to a discussion to gather more feedback and use cases for potential future design work.

@SeeminglyScience thanks for the update!

I would also like to know the status of working group membership / discussions.

A few years ago @SteveL-MSFT asked which working groups I might want to be on. I replied (including this WG) and yet, have still not been "looped in"

Additionally, I have requested that working group meetings that involve a particular feature / issue invite the people to speak. I would have liked to see this happen in this case.

I can appreciate that this fits into a "not now, but maybe sometime" bucket.

I would have preferred some communication on the issue in the past 9 months.

🤷 Better late than never.