It’s stresses the digusting, offensive nature of the stairway
The story is basically saying that we can learn from our elders, because they have been around longer and have more experience than us.
You can see this when it says "the tree is older than you are...you might find stories in its branches".
After Gregor has died and freed his family of his horrendous presence, they can now take a rest for a while and get back to their normal lives. Gregor had been a burden for them in every way, as he stopped providing for them because of his new condition. Because of him, they couldn't leave the apartment and find a smaller one. Because of him, they had to rent a part of the apartment. His unwilling transformation had changed their lives for the worse. Now that he's gone, they have a hope for a better life. They even start pondering on their daughter's potential marriage.
