In my experience, when someone says "what time do you have" they have a device that tells time, a clock or watch or phone, but they're uncertain about its accuracy. I might say "what time have you got?" If I had recently purchased a new watch, and I want to set the time accurately. Alternatively, I might ask a friend that if I was in a room with a clock that I suspected was off by a few minutes and wanted to know exactly what time it was.
Basically, it's shorthand for "what time does your phone/watch/computer have?"
I have lived in Jamaica and in the U.S. What time do you have? is another way to ask for the time. Some people who do not have the time may ask it that way if they want the time. It just depends on the person. It may be a regional saying. I have heard people in Jamaica use it. That is a more british english (despite the accent), so maybe it is a more British saying. I don't know.
For example I wanted to go yesterday. Simple and common but for some weird reason people in Louisiana say I wanted to go ON yesterday. It is awkward and weird but it is just another way to say the same thing. It may be coloquial to a specific location.
Actually I got some answers from google and was a little bit confused. I think I understand it now.
Thanks for all of you native English speakers!