I believe you got the system wrong. The system is not stagnant - it is going to be a lot more likely to recommend you a character you have not gotten. I managed to get Bailmaint and Taria more than once out of the few times I have done the questions. If you have completed all four routes, it probably is unbiased.

This is extra helpful. I understand this particular segment turned many fans off, if not made it very confusing initially back when the game first released. When I got it on the Switch I didn't mind. I was aiming for Urpina, but now I see how that happened. After completing the game with her I was aiming for Taria, which did come out on the first try. But in trying to help my friends before I had beaten the game, I could never reproduce their results.

Now that I was gifted this game the past holiday sale, I decided to look into it again. This time, to try Balmaint. Had no idea he was one of the rarer outcomes just like Taria apparently was. But with that first dropbox link I can get to the character and starting bonus every time.

Many thanks!