Unfortunately there's nothing unusual about people behaving badly on the Internet. Some servers clamp down on unruly users and some don't. If you and the other players in the majority are having an issue, you can try to get the admins in that game to take action, or perhaps convince the author to implement features to help control problem users. For obvious reasons there would be no way to put a button in every BYOND game like you suggest.

Also keep in mind no solution is perfect. If the button you suggested actually existed, it would be subject to abuse by the same people you're having trouble with. They could just as easily report you as a problem. Only a human admin would be able to tell which player deserved to stay. If Roblox has a button like this, all it's doing is telling their admin team to keep an eye on the person to see if they're out of line. (They probably also have penalties for abusing the button.) On the scale of an individual BYOND game, you basically have only the admins that were appointed by the author and/or host, if even that, and unlike a dedicated team they can be called away or distracted or even not present at all.

Ultimately the host dictates what sort of atmosphere is present on a server. Most of them are lax and will allow a lot of bad stuff to go on, but if you find a game server that encourages friendly play and punishes trolling, you can help reward their efforts by spreading the word about that host among other like-minded players so they will join you. Other hosts may see what's going on and try to emulate that same style.