As I recall, it all goes back to the bits in the Radio Regulations that Administrations are required to preserve the secrecy of radio traffic, or words to that effect. The Radio Regulations are international law, and are signed up to by governments like any other international treaty. The requirements date back to when personal telegrams and so on were sent in plain language by morse: these days, it's a convenient weapon for the enforcement agency to have available.
'If any message, the reception of which is not authorised is received, the contents of the message or its existance shall only be revealed to a duly authorised person or a competent legal tribunal'.
As to why not digital, there's a number of reasons. One is the installed base. Another is that digital is either there or its not - but analogue can have a lot of degradation and still manage to get the message over. Similarly, aircraft VHF is AM, not FM, because with FM the weaker signal is suppressed: on AM at least you know its there, and there's a better chance of realising it. Which, I understand, was the original reason for choosing AM for aircraft VHF fighter control in 1939, although it wasn't widely available until about 1941/2. Incidentally, the fact the band is 108 to 136MHz stems from that band having been used originally. After WW2, there were a lot of surplus 4 channel VHF radios available (the American SCR522), and they got fitted in civil aircraft for a while until purpose built equipments with more channels became available. Having said all that, there are moves afoot to bring in digital voice for aircraft control: how it will perform in practice when there's a lot of people trying to talk at once will be interesting. I can see nobody getting through at all, instead of one or two making it.
Still, in modern radio engineering, it's like the quote from Animal Farm, - 'Analogue bad, digital good'.