Licence use report

It should be easy to script. If you are using OSX put this AppleScript in InDesign's startup scripts panel and it will log the current date everytime ID is launched. I'm sure the same could be done with JavaScript, so if you are not on OSX ask in the scripting forum.

tell application "Finder"
    --today's date
    set dt to do shell script "date"
    set LogPath to POSIX path of (parent of (path to me) as alias)
    set LogFile to LogPath & "LaunchLog.txt"
    try
        --add todays date to the log list
        set logtext to read LogFile
        set c to count of paragraphs of logtext
        set newtext to logtext & c & " - " & dt
        do shell script "echo  " & quoted form of newtext & " >  " & quoted form of LogFile
    on error
        --no logfile, make new
        do shell script "echo  " & quoted form of "1 - " & dt & " >  " & quoted form of LogFile
    end try
end tell

Save the code with Script Editor into /Applications/Adobe InDesign CC 2018/Scripts/startup scripts. You will have to set the permissions of the startup scripts folder to allow everyone so the log file can be written. Here I named the script CheckLaunch and launched ID twice: