# Why is probit regression favouring the Gaussian distribution?

Probit regression is based on the model $P(Y=1 | X) = \Phi(X'\beta)$, where $\Phi$ is the standard normal cumulative distribution function (cdf). Would it make sense to replace $\Phi$ by another cdf?

ADDED: If yes, is there any practical, historical, or theoretical reason that explains that the normal (and logit) distribution(s) have been favoured? Is the choice of another distribution implemented in statistical sofware (R or others)?