This approach appears in almost every introductory statistics text. It's easily understood, and it shows how the analysis of proportions is nearly the same as the analysis of means, despite the difference in appearance. The standard convention is to use Roman letters for sample quantities and the corresponding Greek letter for population quantities.
Some books do just that.
However, the Greek letter p has its own special place in mathematics. There's really nothing new to learn to compare two proportions because we know how to compare means. The proportion having a particular characteristic is the number of individuals with the characteristic divided by total number of individuals. Suppose we create a variable that equals 1 if the subject has the characteristic and 0 if not. The proportion of individuals with the characteristic is the mean of this variable because the sum of these 0s and 1s is the number of individuals with the characteristic.