This is how I look at it, from the perspective of a person watching anime. The two big outcomes that could have happened were: Yuuta gets evicted, and he and the girls have to find a new place to live on top of maintaining a healthy lifestyle; Yuuta does not get evicted, and he and the girls still have to maintain a healthy lifestyle. If he had to be evicted, there would be an episode where they all moved, the audience hates the landlord forever, everyone moves on. If he doesn't get evicted, skip the moving episode, the landlord isn't completely hated, everyone moves on.
Yes, you are correct that, statistically, people who have been in the position to be evicted probably are unlikely to have that decision rescinded. However, being unlikely does not make it any less realistic. I guess this is the point I was trying to get across. I feel that I did not have to go through any suspension of belief in order to process the end result. With your own experiences, though, I do understand that this isn't true of all viewers.