Was reading a topic on another forum about adding more combat into the game. How would the game break if only these two objectives are available? And that the only way to win is through Domination or Supremacy ?

It would certainly add combat, that's for sure. But I think it would increase the game's length quite a bit. And certain races would probably be at a severe disadvantage (because of weaker fighting skills, etc).

However, if those are the ONLY two objectives in play, other players won't be focusing on the other objectives and would be able to be more military driven.

Also, this would render the Imperial cards and the Bureaucracy card somewhat useless. Imperial II would be less so, as you could use it for the free build (which nobody else could do), but Bureaucracy wouldn't have a point; and the problem is, the Bureaucracy secondary is the main way to get ACs other than the status phase (or choosing Assembly).

I would definitely recommend playing with leaders if you want to go this route. The races who are poorer at combat usually have some useful leaders, like diplomats and spies, that could be essential in foiling their stronger enemies' plans. I'd also play with DS in the hopes that random luck would favour the meek (although there is no guarantee of that), but then again I always play with DS anyway.

Sigma's comment about increasing the game time is the major factor to consider, though. Playing a regular 8 player game with all normal objectives intact has clocked us in at 13 hours to completion. Allowing only Domination and Supremacy would probably result in a game that literally CANNOT be finished in one sitting. Make sure you have a decent sized table that you can leave the game set up on for a few weeks!