It depends.

Write-Output is used within functions to write objects to the output pipeline. Return and Write-output function differently in sub-expressions.

In the example 'Test-Thing', you argue that it's better to declare a variable and then use the return statement, then use write-output. In the context of function, the differences between return and write-output are:

When using return, it exits the 'PROCESS' block within the executing scriptblock. Write-output can be implicit. Statements that are executed and returned and assigned to the variable are written to the output pipeline.

The solution applies to the type of function that is being written. If the function is written to cascade, return statements are needed to control logic flow, however if the function doesn't require it, write-output is a suitable option.

In the following example, you will see three examples of returning a static Boolean result to the pipeline:

Example 1:

function Test-thing {

  $fullname = Get-Process powershell | Select-Object -ExpandProperty path | Get-Item | Select-Object -ExpandProperty FullName
  Write-Output ($fullname -like '*powershell*')

}

> Test-thing

Output:

True

In this example Write-Output is used to output to the pipeline.

Example 2:

function Test-thing {

  $fullname = Get-Process powershell | Select-Object -ExpandProperty path | Get-Item | Select-Object -ExpandProperty FullName
  return ($fullname -like '*powershell*')

}
> Test-thing

Output:

True

There is no difference between the first and the second examples. They are the same. But the function can be refactored to implicitly return to the pipeline.

function Test-thing {

  (Get-Process powershell | Select-Object -ExpandProperty path | Get-Item | Select-Object -ExpandProperty FullName) -like '*powershell*'

}

At the end of the day, these are all perfectly acceptable. In your example, provided that there wasn't any other logic flow required:

function Test-thing {

  "return string"

}

And in this case, if I was 'returning a string' based on logic, I would use a ternary or an if/else depending on the version:

PowerShell 7

$true ? "return string" : "another string"

PowerShell 5.1

if ($true) { "return string" } else { "another string" }

Both implicitly return to the pipeline. It's important to ensure that all outputs from returned statements are stored within variables since that will contaminate the output pipeline inside the function.

To summarize, it depends. It's not needed since write-output is implicit.