Why so many abbreviations in NOTAMs, etc.?

Why are so many things abbreviated in NOTAMs and other similar documents?
Even words that aren't very long to begin with are often abbreviated, saving
only a letter or two. I can't think of any situation today in which bandwidth
would be so severely limited that saving a letter or two would make a
difference, so I assume there is some historical reason for the abbreviations.
Were such messages transmitted by Morse code or something in the past, or is
someone still transmitting them that way (or over some other extremely slow
channel) today?

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