Are you holding the choke when you try to start it?
Is your choke functioning? (check to make sure the cable is hooked up and adjusting the choke on the carb)
Have you replaced the fuel lines? The fuel lines can dissolve internally and make a green goo which clogs up the carbureator and can make the engine run lean (and destroy itself).
Even with a properly rebuilt carb, you have to pull the choke all the way out when the engine is cold and crank for a little while. My GTS starts after about 5 seconds of cranking when cold, and instantly when warm. 3 or 4 15 second cranks is not normal.
It sounds like you may have a fuel delivery issue. If you haven't replaced the fuel lines, do so first. You'll fight carb issues forever. If you're unsure if the lines have been replaced, see if the fuel lines are grey. If they're grey, they're probably original and need to go.
When is the last time you rebuilt the carbs? The fuel pump in the mikuni is a plastic diaphragm with two one-way valves driven off vacuum from the engine. It's a short hose between the engine block and the mag (forward) carb. If that hose is leaking, you may not be getting good fuel pressure.
The next place to look is the small fuel filter inside the carb. If can get clogged and not allow as much fuel through. This can especially happen if you haven't replaced the fuel lines. However, if you're going to tear the carb apart, buy an official, OEM Mikuni rebuild kit and rebuild the carb. Don't buy one on Amazon--go to a reputable 2cycle seller, such as pwcmuscle or osdparts.com). The non-OEM carb kits don't work well.
I rebuilt my carbs on my 1996 GTS and the difference was night and day. It idles smooth, revs well, launches as you'd expect, and starts easily.
Good luck!
P.S. if you're asking why carbureators require a choke, and why they can be hard to start while cold, it's because gas can condense inside a cold carbureator and intake manifold, causing not enough fuel in the mixture. You have to covercome that condensation until the engine starts and warms up.