Why do we Softmax at all?
The ratio doesn't take into account the fact that the last layer may have negatives results, in which case the ratio doesn't work, while the softmax does. Another corner case is if the denominator of the ratio is zero.

Also, softmax has two interesting properties: 


It will accentuate the differences between the input and the output, by squashing the lower values and increasing the highest value, which makes the output of the network closert to a max instead of a softmax (note that max is not differentiable and hence cannot be used).
In a classification problem, where a softmax layer is used, the loss function is the cross entropy, which has the form - y * log(y_hat). Turns out that log of softmax is very easy to compute, as log(a/b) is log(a) - log(b) and log(exp(x)) is simply x. That makes softmax more desired.