None of this is the point. The point is he offed a man who up till now has been a loyal ally. Other potential allies are going to notice this. Don't interpret that as meaning Loghain has to die, but killing Alistair will make people wonder about you.
Alistair is not an ally to the Warden, he is a follower who went out of line. A Grey Warden who was willing to betray the oath he took for petty vengeance. The Warden is about to become a general and the first thing the nobles are going to see is a rebellious subordinate going out of line, if you allow it they would think less of you.
If the Warden had turned on Eamon I could agree.
I'm not so sure about this; Eamon has a large following among the nobility; if Eamon claims Alistair is Maric's son, then few will dispute him. Eamon has made the claim, for better or worse,and now it must stand.
Except they did not believe it as Eamon himself pointed out, they only back if you for their own self interests.
It is clear Logain had support of many in the Bannorn, but certainly not a majority. Anora though seemingly popular drew most of her direct support through her father; remember Anora does not have noble blood either. As for the royal army, most of its officers would be nobly born... Indeed if Anora gets the chance she will execute Alistair to prevent the seemingly inevitable rebellion, and end the Theirin line (leaving her as sole royal claimant). Anora's position is fundamentally weak and only tyrannical use of power can preserve it.
Half is half, not a majority but not a minority either. You must personally convince must of the arls and strong Banns to convince the Bannorn to side against Loghain in favor of the Warden. As for the royal army, not likely though that depends on what you see a royal army.
There is no unified military in Fereldan given it's a feudal system where which lords brings men to fight for the King and Queen. The Royal Army only counts soldiers fighting directly under the banner of the crown and they would be like Cauthrien: Loyal, well trained and capable.