I think it would be good if, as we know you start in prison, that a dragon destroys the prison and you escape with the aid of someone else who knows what the Dragonborn should do. He basically tells you that you need to kill dragons, then dies. He also mentions the greybeards, introduces you to the shouts, but thats it. This leaves it to the player to do the main quest at the same time as not doing it. You can explore as you want, and every now and then a dragon finds you, and you kill it. Your doing your job. If you want, you can go to the greybeards and then carry on proper, but it isnt forced upon you.
I'm sorry, but that sounds absolutely horrible.
I agree that at some point in the main quest line, you should be able to figure out that you can kill dragons and drain their power, and then are left to go out and do it at your own pace (and level of experience), and I agree that your ability to kill dragons and take their powers should not be limited by progress along the main quest (even if the number of dragons is).
However, I do not think the proper way to do it is to lay it all on the player in the tutorial... what a terribly bland and uninteresting plot... there needs to be plenty of detective work, socio-politico-cultural intrigue and discovery, and at least one shirt-less drug addict giving you orders.