Applying the independence of irrelevant alternatives (IIA) is an inherent assumption in multinomial logistic regression but not binomial. Is it therefore okay and possibly better to use $K$ binomial logistic regression models instead of multinomial logistic regression when handing a multiclass classification problem with $K$ classes? Is this approach typically employed or not for any reasons in any scenarios (e.g. predicting elections)?
The primary concern I can think of is interpretation of probabilities. The $K$ binomial logistic regression models would allow one to understand the relative probabilities of class $A$ versus not class $A$, but would not have easy comparison of the probability of class $A$ versus class $B$. To compare the probabilities, some kind of alternative method (e.g. apply softmax function) would have to be employed, but perhaps this is just as misguided as the IIA assumption.