I don't think this is precisely true, "mobile telephones are specifically exempt (otherwise we'd all need a licence to use one)". The deal is that your cellphone operates under the license of your carrier. You are not really the control operator of your cellphone, the cell provider controls when your phone transmits, its frequency, and power output. All you can do is turn it on and off.
If cellphone frequencies were license exempt then we could build "cellphones" that call point-to-point direct without a cell carrier as the middleman.