It's not just a "cool" thing. There is historical precedence for this pattern. Hearing Americans have always said, "19-39", "18-12", "14-92", etc. We said, "17-76", not "one-thousand, seven-hundred and 76." ASL follows the same pattern.
When we use year dates, we aren't using the date as a number but as an identifying name. The name is a combination of century (14th, 18th, 20th, etc.) and specific year ("36", "99"). Since the first two numbers represent a century, the "00" is understood.
We should have really been using the "20", not "two-thousand" the whole time.
"17-hundred"
"18-hundred"
"19-hundred"
"20-hundred" (not "2,000")
"17-0-6"
"18-0-6"
"20-0-6"