Also, if both you and your opponent are going for a neutral territory,
someone proved quite well that it is still best to attack last if you want the territory.

And if you and an ally are both going for the territory or the army-killing of a mutual enemy, knowing that your army will go first or last could make all the difference in avoiding a friendly fire issue. :)

That is not correct. Sometimes you want to attack the nuetral first. Depends on the size of your as stacks and the size of the nuetral.

There is no rule of thumb. The settings matter

yeah sometimes you want to take neutral with 4 armies at start of the game to block opponent's bonus
sometimes you want a territory first because it has big strategic value,and sometimes you want a neutral just to ensure you get your bonus completed