I don't really understand why making an ordinal response variable binary is a bad thing. In fact having read logistic regression books I came to the conclusion that making an ordinal response variable binary was safer in terms of interpretation or violation of assumptions.
"When the dependent variable is ordinal or continuous, classification through forced up-front dichotomization in an attempt to simplify the problem results in arbitrariness and major information loss even when the optimum cut point (the median) is used. Dichotomizing the outcome at a different point may require a many-fold increase in sample size to make up for the lost information187. In the area of medical diagnosis, it is often the case that the disease is really on a continuum, and predicting the severity of disease (rather than just its presence or absence) will greatly increase power and precision, not to mention making the result less arbitrary."
"When the dependent variable is ordinal or continuous, classification through forced up-front dichotomization in an attempt to simplify the problem results in arbitrariness and major information loss even when the optimum cut point (the median) is used. Dichotomizing the outcome at a different point may require a many-fold increase in sample size to make up for the lost information187. In the area of medical diagnosis, it is often the case that the disease is really on a continuum, and predicting the severity of disease (rather than just its presence or absence) will greatly increase power and precision, not to mention making the result less arbitrary."