Can a higher frequency EM signal encode more information?

Or to illustrate it even more clearly, how many can you fit in below 100 MHz?

But that’s cheating. How many 100MHz bands can you fit between 0 and 1GHz? How many can you fit between 1GHz and 2GHz? You changed the questions.

Another advantage of higher frequencies is that you can build high gain antennas, i.e. highly directional antennas that beam the signal in a particular direction. This is used in cellular telephony to create multiple sectors by forming beams at different angles, thus expanding the number of customers who can be served and increasing the received power at the same time. Of course the cell phone has limited ability to form a beam in the reverse direction, since it is smaller and it’s angle is not fixed. However, the receiver in the base station also benefits from the directionality. The so-called antenna gain is the same in both directions.

This is analogous to using a telescope at optical frequencies. The bigger you make the objective, the more directional it becomes. At either optical or radio frequencies the available antenna gain depends on the ratio of size of the objective/antenna to the wavelength.

Not really.
Different frequencies require different technologies and have significantly different characteristics. We tend to break the frequencies into decade bands, and place the breaks based upon their wavelength. So the Low frequency band aka LF is 0.3MHz to 3 MHz (AM radio stations are in here), High Frequency band aka HF, is 3 Mhz up to 30MHz (100 metres to 10 metres), very high frequency - VHF, is 30 MHz to 300 Mhz - 10 metres to 1 metre (TV and FM are in here), and so on though ultra high frequency - UHF, super high frequency, and then the letter bands, X band K band and so on. Each is a 10 times increase in frequency over the next, and a ten times shorter wavelength. The wavelength is a significant clue as to the utility of a band, as it governs such things as antenna size and design.

Each time we need to invent new technologies to cope with the physics. Once I have the needed technology to cope with 1Ghz I can use it at 2GHz easily. But the technologies used for the entire bandwidth up until 1GHz won’t work. That 0.00001-1GHz bandspread involves multiple generations of technology each with a huge variation in scale and operating characteristics, whereas that 1-2Ghz band is just a small increment in technology.

That first band from say 0.00001 Ghz to 1Ghz covers long wave bands used for early radio communications, the AM radio bands, all what we called the short wave bands, used for all manner of communications including shipping, aircraft, the FM radio band, all the terrestrial TV transmissions, a lot of cellular phones, and so on. A century of technological progress, and still containing a huge amount of valuable capability. The 1-2Ghz band can contain all of the information that entire band does. But it can’t reproduce the functionality. You can’t use it for almost any of the prime reasons we use those longer wavelengths - like long distance propagation. 1Ghz is line of sight only.

We don’t fit any 100MHz bands in the 0-1GHz band - because we could only ever fit 10 of them. Yet right now we fit many hundreds of services in there. We fit the entire AM radio band inside 0.8 MHz of bandwidth. We fit the entire FM radio band inside 20Mhz. Notice how the width by which we break up the bands is based upon the base frequency of the band in question. We break each up into enough chunks to get a sensible number of allocations in each useful band able to make use of the characteristics of that band.

If some cellular phone company came along and demanded that they be allocated the 0-100MHz band, they would be demanding that they be allowed to take over the bandwidth used by all the AM stations, most of the terrestrial TV stations, the marine and aviation short wave bands, half of the FM radio band, and a whole host of other capabilities. Yet they could use 1-1.1GHz and have the same capability. Moreover, a system that tried to use 0.001-100MHz would span many decades of wavelengths, and require almost impossible step changes in implementation and antenna design.

Bottom line, it makes a huge amount of technological sense to allocate bands based upon a percentage of the basic frequency that band works in. It makes no sense to talk in fixed bandwidth allocations across all bands.