In the ship designer I can delete my ship designs. I can not delete the base game designs and I have to mark them obsolete EVERY time I load the saved game.
Your right.
You can however filter all of them out at the start of game by choosing the left most icon at the top of the shipyard screen they are left to right are show all, show core only, show Custom only.
As for deleting the core ships it will not work as every time you verify file or update, they will return
You also can create your own ship set and replace the core ships
Not sure how as I have never in 30+ years of gaming wanted to delete the games unit file permanently.