The thing is, there is supposed to be dragons flying around. If players never encountered a dragon people would be saying, "What the hell Bethesda? I'm dragonborn and don't have any dragons to kill!"
Here is the way I think it should work. Since we need 60 Souls for the Shouts, then that is the target.
1. During the MQ, Random Encounters happen like they do now, even near or in cities. Gives a sense of urgency to the events and this goes on as long as the MQ is still open.
2. Word Walls or Dragon Priest Locations or Lairs will have dragons, even after the MQ, until they are killed. Word Walls that are in Interiors would spawn a random attack somewhere near the entrance/exit to the dungeon These location dragons don't respawn. However, these dragons would not bother the towns and or most settlements because they are not that close to them. This is an effort to preserve NPCs while giving more dragons to battle.
3. Radiant Quest Dragons (Bounty Quests) will show up even after the MQ . These are almost never near a town anyway. Again, to preserve the NPCs.
This would give more than 60 Dragons to unlock all the Shouts, if someone wanted that. And, they could battle Random Dragons as long as they want to keep the MQ alive, and even after the MQ, the fixed locations would give enough dragons to feel like one has done something. Yes, the dragon threat diminishes as the game goes on, and is greatly reduced after the MQ, but there are still plenty of them to do battle with.
More importantly, it gives satisfaction that you have actually done something about the dragon menace and not just one dragon.