If you had another dollar, then the value of the next dollar in utilons would decrease. Unless you're both an egoist and terrible with money, it will only be a slight decrease. After all, a dollar isn't much compared to all of the money you will make over your life.

I do not think that the fact that utilons do not add up linearly means that the conversion is not useful. For one thing, it allows you to express the law of diminishing marginal utility.