He's a coward and the Dragonborn is the one person who can theoretically defeat him, throwing dragons at the problem is one of his only options without actually dragoning up and being brave. If he attacks directly he risks actual harm, if he attacks with hit and run tactics or indirect methods then he loses face in the eyes of the other dragons for being afraid of the Dragonborn, if he sends dragons he can kick the can down the road a bit while hoping an underling gets lucky and explain it as the Dragonborn being beneath his concern.
I do think you have something with him being there to prevent Ulfric's execution to prolong the civil war and get more souls to eat, but we don't know what Alduin actually knows at the time. Does he know Ulfric is the leader of the rebels? Does he even know there's a war on at the time he attacks Helgen? How long exactly has he been back by the time of the foiled execution?
If he could still percieve things while in his time out, or has been back for a little while, then he'd probably be aware of the general circumstances and move to maintain the status quo that benefits him.
If he's not aware of what's going on then throughout the province the only reason to show up at Helgen is the Dragonborn. Or generally being an *******, which is always an option with dragons.