It could be for a myriad of reasons, first and foremost I think it's about pride, even though his financial situation was burdensome to Yeomin, he felt proud of facing the problem head on. Tbh I think he isn't able to accept help from the way his childhood was. Then, I think it's not only that but also him wanting to be on equal ground with the top. He probably would've felt like a plaything otherwise or like he was whoring himself out to him to pay for his tuition which comes back to point one, it would have hurt his pride. But to be fair, you don't want to depend of anyone economically precisely for the reasons we're about to find out in future chapters (that I assume will have the top controlling Yeomin or at least trying to and Yeomin not being able to leave)
Cuz he'll be no different from a sugar baby or lets say a prostitute and Yeomin knows it. Taesoo wants to sleep with him and Yeomin stays cuz he like him. They are fwb. They're both in it for the sex (and Yeomin, for his feelings) But if taesoo only wants to sleep with him and pays for his life, how is Yeomin any different from a sugar baby? Yeomin has dignity.
I dont have much but i wont ever be a sugar baby. I guess the same goes for you irl. Lets just say, the same goes for yeomin. Not everyone wants to be a sugar baby or a prosti

Idk, I'll never understand why the ml's don't want any help. I would be glad to let some rich CEO daddy pay off all my debt if they offered