I guess after Bitcoin reached its first ATH in 2017, some mainstream Media started referring to ALTs like XRP and ETH by the abbreviation of crypto. I started hearing crypto from that time, though I may be wrong this is my opinion.
Plus it is easy to write crypto than cryptocurrency and also it is easy to pronounce.
I have come to the conclusion that the term "crypto" came about because people wanted to use a more attractive name than "altcoins." The maxi in me will continue calling all "cryptos" altcoins! I will call coins I respect by their actual name, but as a group they're always altcoins.
I do personally refer to cryptocurrency as it is, not crypto. Kind of irritated when I hear others refer to crypto as cryptocurrenices, but that is the way how the word got into the mainstream people, even in the terminology way the word is incorrect, people are getting used to the word crypto definitively.
If we try to take a look at Google Trends[1], we can see that the keyword crypto getting its attention in 2017. And if you see the related queries, people added up crypto as their search keyword when they searching up for something. That's may explain people write crypto because it shorter.
[1]
https://trends.google.com/trends/explore?date=2017-01-01%202018-12-31&q=crypto