I am fully aware of climb gradient requirements.
You do realize that putting "NO SID" on the flight plan just means the controller's going to have to read it to you verbatim, longhand, right? It doesn't have anything to do with whether or not you can fly it.
NO SID = "I don't HAVE the SID", not "I can't ACCEPT the routing specified in the SID".
Any time you can't comply with an ATC clearance it's your responsibility to say so. "NO SID" is not the right way to do that.
So you ask for another SID, or ask for the ODP, or just don't depart that day.
"NO SID" was born in a time when the SIDs and STARs were physically in a different printed book than the approaches. So it was reasonable and common to not have them.
However, I'm trying to think of a valid, practical reason nowadays to not have them and therefore file "NO SID". They're in the same book as the approaches for the airport, just a few pages away. If you're using an EFB, they're probably already downloaded. If you're just printing a few charts off the internet, well, you had to intentionally decide to NOT print off the SIDs so you had to have at least have looked at them to determine if you needed to print them off or not.