> the German word for "entertainment" is "Unterhaltung"; thus it can be argued that the purpose of entertainment/Unterhaltung is "unten halten"

No, that would be "Untenhaltung", which isn't an actual German word, but could be.

"unterhalten" in German can both mean to entertain (however, not as in "entertaining a notion") having a conversation, as well as "to maintain". It has several meanings, all of them positive.