Why do the Japanese greet each other with “Konnichi wa” (“Today!”)

This was one that really puzzled me in my first couple of years in Japan and then I completely forgot about as it got older. According to Japanzine, it used to be used in longer phrases like “Konnichi wa atsui desu ne” (“It’s hot today today, isn’t it?”, common nowadays as “Kyou wa atsui desu ne”) and just got shortened as time passed.

Japanzine is admittedly not the most academic of sources,┬ábut this seems to be fairly common in greetings, as in “Ca va (bien)” in French, so makes sense to me.