Why dont these 2 branches have a more prominent role in the Halo Universe. After given the UNSC is modeled after the current day USAF(armed forces not airforce) one of the main mission airforce is space related missions having several dozen satellites.
and why doesnt the army fight alongside the marines more given they have their own ships?
Because the UNSC Army tends to play a more defensive role, they are the ones who stay on planets and defend it to keep it safe. The UNSC Marines and ODSTs are the ones who take a more offensive role, taking the fight to the enemy and unknown worlds. Which do you think we do more of in Halo?
And the UNSC Army did play a important role in Halo: Reach. All the troopers in the game were Army and even some Air Force.
The UNSC Army and Air Force are there for mostly defensive roles to protect the colonies. The Marines and ODST’s are more in the offense department, and I think the Navy are in both departments.
In Reach, most of the troopers you see in the game are Army Troopers, and I think theres some Air Force troopers in Long Night of Solace on Ardent Prayer. There were Marines towards the end of the Pillar of Autumn though. But I do remember hearing somebody calling the troopers in the Boneyard area Marines even though they looked more like Army Troopers.
To me, it seems like the Army and the Airforce are “local” forces. They stay behind on a colony to assure its safety, while the Navy transports Marines for offensive operations.
I think the reason why you don’t see them more often is mostly because we’re rarely on a human colony defending it from the Covenant.
Also, according to Palace Hotel, Army troopers WERE present during the Battle of New Mombasa.
Would be cool if the UNSC Army still maintained a 75th Ranger Regiment 
any indication why UNSC army personnel are referred as “troopers” instead of just soldiers?
I would assume because the UNSC is a “naval” force… So they would always have large complements of marines just as the USMC of today looks after are navy those marines do too. So that probably explains why we see more marines then army/air force.