Why do so many people fight with the ring coming up on their rear ends?

You are completely right - people should run away, when the ring is coming. There are emotions, when you are fighting at the edge - running from the ring, getting kills, being under fire and so on. Its fun i must say, but also an unnecessary risk. Players should always prioritize the ring.

Its also often due to the poor planning and the urge of getting those kills, especially in ranked. Many random players cannot let go the fight. Well - if you say it through the mic then maybe they will listen, but with only pings, good luck with that.

Although waiting for the ring to close at the border and waiting for people to come is a good idea. Then you will know, that from at least one direction enemy won't come. In my opinion the safest way to play, if you cannot estimate, how many squads are nearby.