This is not really about what a parable is and isn't. It's about Christendom's love of hell and their propensity for adjusting scripture to meet that desperate need. The fact that most Bibles falsely contain the word, "hell" is a travesty.
I can play this silly game, also. #1 (below) is the only one called a parable, so #2,3,4,5 cannot be parables - or, maybe the real truth is that Jesus Christ reasoned that saying it once at the start would apply to all 5 fictitious stories He planned on telling, one after another. And, #3, 4, and 5 all start out with, "a certain.....", but #1 and #2 don't. Therefore, #1 and #2 can't be parables - I guess Christ was wrong about #1. And, none of them mention the Kingdom, so I guess none of them can possibly be parables, according to your logic. These 5 parables all follow in order, with a short 5 verse break between 4 and 5, while Christ rebuked the Pharisees. All of Luke 15 and 16 are parables. To say otherwise, is a corruption of the scriptures. Usually, people use the absurdity that #5 isn't a parable because Lazarus' name is used. The absurdities that people dream up to distort scripture, so it will fit their agenda, is always amazing to me.
1- Lost Sheep - Lk 15:3-7, Called a Parable in vs 3
2- Lost Coin - Lk 15:8-10
3- Prodigal Son - Lk 15:11-32
4- Dishonest Manager - Lk 16:1-13
5 -Lazarus and Rich Man - Lk 16:19-31
Your reasoning on the topic is a very common one that reeks of the traditions of men, similar to those that believe in the 100% pagan concepts that (A) man HAS a soul, even though Gen 2:7 eliminates that possibility by saying that man IS a soul, and that (B) unbelievers are tortured by our loving God, in fire, forever, 24/7, even though Christ died and thus paid the entire debt for the sins of the entire world - 1 John 2:2. Here's a good discussion of that verse.
https://www.bibleref.com/1-John/2/1-John-2-2.html
A reason that some people say L&RM is not a parable is because they love the idea that people less pious than they are will be punished. In some churches, those that don't believe in hell are considered unsaved