# OLS Consistency for Count Data?

Why would we choose Poisson / NB regression (GLM) over OLS for fitting count data?

Is there a way to show that OLS estimator would lost it consistency and asymptotic normality for count data?

I'm asking this because my sample size ($$n$$) is extremely large, and I can always increase it when needed (so that the asymptotic behavior of OLS estimator with count data is all that I care about).