Do you think Skyrim would have been a better game storywise? Obviously, we're assuming the marketing was about the war in Skyrim and not about dragons. You could still be Dragonborn as in terms of lore, the Gods send down Dragonborn when the world is in need.Frankly, a World War in Tamriel seems reason enough. The Greybeards also exist and they can train you instead of you absorbing dragon souls.

So the story will lead to you to choosing between Stormcloaks or Empire. And since TES loves the pure evil bad guy, we have the Thalmor instead of Alduin. In that regard, let's assume that there are memorable characters on both sides. Like Tullius and Ulfric were heavily developed along with one or two of your comrades.

Let's also assume that the execution was stopped by a Stormcloak rescue party or some other force.

They would have needed to make it SEEM like a civil war was actually going on.

No in my opinion the story makes more sense with dragons. The Hero of Kvatch and the Nerevarine were ordinary mortals. Being Dragonborn in just a Civil War quest is too OP and doesnt make sense in my opinion. If the story went with that Main questline then he would have been similar to the Hero of Kvatch as an ordinary Mortal. The only difference between Dragonborn and a regular mortal is the inborn ability to learn shouts in an absortion of Dovah souls. Any mortal can use shouts.