The problem isn't limited to Logic Pro. It appears to occur when an assistive app launches a document. If the document’s app is not running, the app launches, but doesn’t open the document. If the app is running, error -1703 appears. This AppleScript demonstrates the issue.
BTW, you won't have any problem running the AppleScript if you're using macOS 12.2.1 or older. It's simply a matter of enabling access in Security & Privacy prefpane. There may be a way to bypass it in 12.3 as well, but I haven't found it yet.
Here, try it yourself. Script Editor.app is in /Applications/Utilities. Don't forget to use TextEdit.app to create a file named "richtext.rtf" on your Desktop first.
set rtfile to alias ((path to desktop as text) & "richtext.rtf")
tell application "Finder"
activate
open rtfile
end tell