How range of the signal increases when modulation is done?
I think that you are interpreting the Friis equation to mean that RF signals carry for less distance than lower frequency RF signals. The “path loss” term “predicts this”.  

The first point which is still confused of why we modulate should be fairly obvious, because we don’t want a 5000 meter antenna. One also uses modulation with amplification.  One also needs to be aware that frequency spectrum is regulated. In the US the FCC is not tolerant of unlicensed transmission so no signal regardless of carrier frequency will carry if you are in jail. 

The Friis equation covers lossless spherical spreading just like the homogeneous wave equation. 

https://en.m.wikipedia.org/wiki/Wave_equation

The wave equation predicts that the signal amplitude from an ideal point source drops off as $1/r$ and if that ideal point source has managed to radiate a signal there is no frequency dependence on the electromagnetic field. 

The Friis equation doesn’t predict electromagnetic field behavior. It predicts the voltage at the output of an antenna. Path loss refers to the path loss with respect  to an antenna with a fixed aperture where voltage does drop off with the carrier frequency.  

For someone like myself who started out as a SONAR engineer, the term “path loss” is an unfortunate choice. 

Terrestrial RF propagation almost never conforms to the physical assumptions which the Friis equation is based on. It does have `relevance because it is actually useful as a first order heuristic.  Higher frequencies are more susceptible to scattering and shading than low frequencies. 
Low frequencies penetrate buildings deeper. High frequencies tend be favored in line-of-sight applications. 

There are other reasons why we want to use a modulated carrier. There isn’t a deep theoretical contradiction in play. 

Essentially your conception of Electromagnetic attenuation is a bit too simple. Waveguides for instance have a characteristic known as the cut off frequency. A field has to have a frequency above the cut off frequency to propagate. Photons are electromagnetic waves and they travel billions of miles. The wavelength is not in itself the cause of attenuation, it is the interactions with matter which have the various effects