Because one single frequency cannot transmit any information.
The signal would only contain a single frequency, if that frequency does not change in any way – the same amplitude, the same phase. Of course, unchanging signal cannot carry information.
If you change the signal in any way – it will create sidebands: frequencies slightly above or below the base frequency. The faster you change the signal – the wider the sidebands will be. Switching the signal on/off also counts: the faster you switch – the wider the sidebands will be.
Those sidebands are not some side effect that can be filtered out – they are fundamental to the change. If you filter them out – all the change in the signal (and all information) disappears.
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