Why can't we simply use ordinary $R^2$ in logistic regression, as we do in linear regression? Domencich and McFadden seem to imply that heteroskedasticity is an issue:
but I don't understand why. In linear regression, homoskedasticity is an assumption (in max. likelihood the variance is typically not considered a parameter to optimise), but why it is an issue for calculating a measure of fit?
Below is a plot from my simulations, for normally distributed classes of different sizes and variances:
McFadden's pseudo-$R^2$ and ordinary $R^2$ seem to be closely related. I'd appreciate if someone could give an illustrative example for a problem arising from heteroskedasticity or any other justification against ordinary $R^2$.
To avoid confusion: I do not imply using ordinary linear regression on nominal data, and/or calculating squared distances from the straight line. For the purpose of my question I'd perform logistic regression, which would produce a logistic curve. My question is: Why is ordinary $R^2$, as a goodness-of-fitt measure of that curve bad, or worse than McFadden's pseudo-$R^2$.
P.S. (for all those thinking this question is a duplicate):
Please quote the relevant portion of that allegedly existing answer to show how it answers my question. Also, please consider: If something is obvious to you, it need not be obvious to others.