上, literally "up/on/above/...", gives an image of going up and reach something or going up up and up to a certain degree/extent.
With the going-up-and-reach-something image, 上 implies transition and gives a sense of "starting to..."
Without 上 it's just only a state of being or a fact.
愛上=fall in love with...(=start to love...)
愛=be in love with (=be in a state of loving somebody/love)
喜歡/喜歡上is a similar case as above
當上=become/come to be (followed by an occupation such as teacher 老師, doctor 醫生...) (start to be)
當=1.be (can also be followed by an occupation, implying your character/role in a society, so oftentimes it is followed by a place or an area, as in, 我在學校當老師(I'm a teacher in school.) or 我在那間公司當老闆(I am a boss in that company.). Otherwise, if we are saying "I'm a teacher" without "in school", we would use 是 instead of 當, as in 我是老師。
2.play (followed by a character/role in a play, show or game)
閉上=close (the subject can be a person or eyes)
閉著=be closed, leave/keep (one's eyes) closed (the subject can be a person or eyes)
With the going-up-up-and-up-to-a-certain-degree image, it implies how far your act has gone, or how well you have done the act. I think it's the case of 過上好日子
...睡上三天 (...sleep for up to 3 days.)
...吃上十碗飯 (...eat up to 10 bowls of rice.)
So let's just say 好日子 is a goal and you want to go up and reach the goal, you want to live up to the goal, so you use 過上 instead of 過.
So when you use 過上好日子, it's like you have a goal of 過好日子 and you want to be able to do it.
When you use 過好日子, you are merely expressing a truth that's already there.