I am not suggesting that there is a non-classical model that accurately explains the inside of black holes, I am saying that due to our inherent lack of any evidence we should not be immediately discounting the models that work exceptionally well where we do have evidence just because they give us results that feel weird to us. Quantum superpositions were also widely rejected early on because they seemed impossible to meaningfully interpret, and yet now we can make computers do maths with them

You don't look at an equation that divides by zero and think, "maybe someday this will make sense." It will never make sense because it will always be undefined, and you need to start looking for your mistake.

This is like saying that the equation of velocity = distance divided by time doesn't make sense because if you travel somewhere in zero time then you have to divide by zero. The equation is correct and has physical meaning, it just so happens that moving somewhere always takes some time. We can understand just perfectly what moving somewhere in zero time would be, we just don't know of any way to make it happen. Loads of useful and practically-applicable equations have vertical asymptotes. Maybe there's something that prevents the inside of a black hole from collapsing to an actual point. Maybe space-time really does just collapse inside the black hole. The model would still be useful and mostly accurate, just incomplete