This question was answered in the comments:

If you add two points with $Z_1=Z_2=1$, the resulting point will (in general) have $Z_3\neq1$. Given that we typically do a full addition chain, and not just add two points together, what is your stategy when it comes time to do the second addition? – poncho

 

In other words, the drawback is that it only works when $Z_1=Z_2=1$. :) And of course you must normalize the resulting $(X_3,Y_3,Z_3)$ if you want the $(x_3,y_3)$ coordinates that point. – Chris

This question was answered in the comments:

If you add two points with $Z_1=Z_2=1$, the resulting point will (in general) have $Z_3\neq1$. Given that we typically do a full addition chain, and not just add two points together, what is your stategy when it comes time to do the second addition? – poncho

In other words, the drawback is that it only works when $Z_1=Z_2=1$. :) And of course you must normalize the resulting $(X_3,Y_3,Z_3)$ if you want the $(x_3,y_3)$ coordinates that point. – Chris