Baby oil as an eye makeup remover?

I started using Equate Baby Oil as an eye makeup remover about one month ago, and I think it works wonder! It easily removes eyeshadow and mascara while leaving skin moisturized and soft. Oh, and it's pretty inexpensive compared to my usual makeup remove, Klorane Sensitive Eye Make-Up Remover (around 12$). But I've heard that it can also clog pores and cause breakouts, as the skin around eyes is really sensitive. Well, I haven't experienced those effects yet, and I don't see why it would happen if I make sure to wash my face and completely remove the baby oil after removing my makeup (as I would do with any other makeup remover, anyway). What do you think? Is it okay to use baby oil as a makeup remover, or should I use a product specifically designed for this use?