That is a talking animal with the intelligence, self-awareness, and emotional capability of a young child and/or adult YouTube commenter. OK, fine, we can leave his Scooby-snacks alone ... except that, have you ever seen a full blown horndog on a rampage? They develop an aggressive streak and lose interest in anything but getting their rocks off. Bear in mind, this isn't some dinky ass Yorkie waddling around with a red rocket. Scooby is a sentient Great Dane.
That's up to seven feet and over 200 pounds of uncontrollable, animalistic sexual thirst and destruction paired with a human-like brain. We have a word for someone with that behavior, and like most of Scooby's vocabulary, it begins with "R."
So yes, Scooby-Doo is more or less a werewolf sex offender with the IQ of a shoe. Can you neuter him? And how the f**k do you even broach that topic of conversation with him? And it's not like you can trick him into going to the vet and hope he forgets after a couple of weeks of g-g-ghost chasing. He knows. He knows.
"You rook my ralls, Raggy! YOU ROOK MY RALLS!"
Best case scenario, you have a neutered Scoob breathing through a hose connected to the Mystery Machine's exhaust pipe. Worst, you have a canine Varys (with way more hair and a way lower vocabulary) silently plotting to strangle his "friends" one by one with Fred's ascot.
Although, this would explain why people started disappearing in the later seasons.