Very good, but if he hadn't been last man, it wouldn't have been DOGSO, would it? Imagine an appeal (if you could). "Were there other defenders between him and the GK?" "No, he was the last man..." Or " No, there were no other defenders in a position to challenge him". "You mean he was the last man?"
For a "freethinker" you seem remarkably hung up on avoiding a free understanding of what the words in the laws mean. Are you channeling the former poster who objected to the two-word expression "foul throw" in favour of "incorrectly-taken throw in"?
Anyway, I support the idea that "a goal may not be scored if the ball is directed into goal by an attacker's hand or arm; if , ITOOTR, the action is deliberate, the offender must be cautioned, and a DFK awarded, otherwise the game is restarted with a goal kick."