They can't, and I'm surprised the officer wasn't aware of that. Confirm the person's ID, hand them the papers or sit them somewhere and tell them, they have been served. Process-wise, all that matters is confirmation to the court that the person is aware of and was given possession of the documents. If they don't like it and set them on fire, that's not the court or the server's problem.
I think there's also generally a process for someone avoiding being served. Ie if you can prove they're trying to avoid being served, that is per se evidence that they are aware they are being served and can be considered as served. Iirc, it's not preferred because it's way, way cleaner for the court to have a signed document but they can and will do it.
Legalities aside, this is why you'd normal hire someone to do this. The cops don't want to be involved, and especially so for YouTube drama. Hire someone completely unrelated who can show up, be completely emotionally detached and do the "I'm just trying to do my job, man" schtick. They're also much better for contested servings. If one party says the other got papers and the other denies it, there's a "he said, she said". If you hire a professional who doesn't care about the outcome of the case then it carries a lot more credibility.
The cops even tell Ben to get a process server, and he points out to the cops that yes, he has brought the exact person they described, she's right there in the car with him.