For AM, doesn't the amplitude of a wave naturally decrease as it travels, unless it's incredibly focused?

I would imagine the data relies on the relative sizes of the waves, not the exact 'real' size. Half the amplitude will be half the amplitude no matter how wide the wave spreads out.

AM waves have wavelengths a multitude larger than FM waves. An FM wave is generally a few meters at best whereas AM waves are often much larger than large buildings.

AM waves are greatly affected by atmospheric conditions(waves move faster in hot air than they do in cold air, meaning the angles of diffractions can vary) and actually tend to 'hug' the ground, their massive wavelengths also mean they diffract around pretty much any structure. AM waves can travel for hundreds of kilometres without issue due to this.

FM waves are far more precise as frequency remains constant after leaving the source, but their wavelengths are also much, much smaller. They are far too small to diffract around the majority of objects, and tend to bounce around a lot, and are not so bound to the earth as AM is. For this reason they lose energy fast and have very limited range.

That is to say, FM waves are not inherently worse at travelling than AM waves. If you transmit an FM wave at a small wavelength it will reach similar distances, the only problem is that FM waves require much more bandwidth than AM waves because they use up frequency space in themselves due to how they work. The higher the frequency, the more available bandwidth, so for the system to work they must be transmitted at much higher frequencies.

So no, AM waves are actually better transmitters compared to FM as they run at a much lower frequency.