I'd say it is sketchy as people say path loss increases with frequency; well it doesn't if you have the same physical antenna apertures (think parabolic dish). Though the formula is called a loss since it's used that way from a circuit perspective, and you treat the antenna gains as not related to aperture, so loss does then increase with frequency.
Yes that frequency term is precisely the sketchy bit. Because of that the equation doesn't conserve energy which is normally considered a bad sign.
On the other hand to do it properly you have throw out the 'reciprocity' of sending and receiving antennas. They are not really the same at all.