Personally, I don't have a problem with draws in competitive events. Two teams clash, they put the pedal to the metal, and in the end neither is able to gain the upper hand and they both go away mad. It happens. My feeling is that it gives both sides incentive to figure out how to gain an edge the next time they meet. But plenty of other people hate them. That's why we have silly shootouts in hockey, and it's also why Overwatch game director Jeff Kaplan said changes are coming that will help reduce their frequency in the game.
"We have changes coming to the PTR very soon. These changes will greatly diminish the number of draws. More details inc. extremely soon," Kaplan wrote in the Overwatch forums. "We're also working on reducing Capture the Flag draws and elimination draws but those changes are further out."
"Extremely soon" is obviously a subjective measure, as no changes have actually made their way to the PTR yet, but for people who hate draws (and based on the comments, there does seem to be an awful lot of them) it's good to know that the wheels are turning. I've emailed Blizzard to ask about what sort of changes it has in mind. We'll let you know when something happens.