Why does higher bitrate requires higher bandwith?
What you describe is called &quot;FSK&quot;, or https://en.wikipedia.org/wiki/Frequency-shift_keying
Also important to note that

you need more bandwidth than just the spread of the states, in order to be able to transition between them. How much depends on how fast you want to switch.
how long you have to hold a frequency before you switch to another depends on how far the frequencies are apart.

All this matters if you are transmitting into a band limited channel, meaning that only a certain amount of bandwidth is available, either by regulatory limits or by physical limits.
Consider the &quot;Talking Tube&quot; or &quot;Speaking Tube&quot; used long ago as intercoms on ships, in houses and now in playgrounds. The longer the tube the less bandwidth is available to you and the slower you have to talk. This is separate from attenuation, which requires you to speak louder over longer tubes.
These tubes are a great example of a physically bandlimited communications channel, with lots of reflections and dispersion!
https://en.wikipedia.org/wiki/Speaking_tube
The bandwidth of the tube determines what individual frequencies get through, but also -and this should not be overseen- how long it takes for a switched frequency to be discernible from others. That limits how fast you can switch from one to another.
If you transmit tones (of around 1kHz), the longer the tube the longer you have to hold the tone before the receiver can determine what frequency was sent. Through longer tubes it takes time for a switched sinusoid at the input to start looking like a sinusoid at the output. This is not just a matter of tube delay (pure delay wouldn't limit your transmission rate) but rather due to the reflections inside the tube.
For more details on the bandwidth for FSK see here:

Notice that the bandwidth is &quot;blobbier&quot; than just two spikes at two frequencies, and the total width is more than the just the span between the two frequencies.
https://www.testandmeasurementtips.com/analog-and-digital-modulation-and-modulation-measurements/