Robert Picardo is a gifted actor who does exceptionally well with light comedy. Not sure how he'd hold up as King Lear.
It's sometimes hard to remember but Picardo's Doctor was pretty darn cranky and gruff through most of Season 1, and he brought that personality back when he portrayed Zimmerman later on. I thought it was totally convincing.
Yes, Picardo seems the most at home with comedy as a person but I totally bought his dramatic side too. I never really bought Sisko having a lighter side -- though I appreciated that DS9 portrayed his hobbies like baseball and cooking, he even took his hobbies very seriously! Picard with a light side was convincing but he's still better as a serious guy in my book.
Plus, IMO doing comedy is much harder than doing drama most of the time.