The BSAA isn't enough for all the world's bioterror. In RE5, it's said that they only handle one third of all incidents and in Umbrella Corps they leave outbreak zones alone for years. The whole point of Wesker starting the war on bioterror in 2003 was so his Umbrella could take over the military market. That's why he developed plans for the Albert gun series.According to the file, they have no field teams whatsoever and depended on BSAA soldiers. I think there's really no point in having BU with BSAA soldiers, it is much better to simply use the BSAA for field missions and having BU's contribution in the firearms department.
The BSAA already has a lot of branches scattered throughout the world, having this new and much smaller PMC conducting field missions (the small military presence as you said) just sounds weird when you have something as large as the BSAA. That's why I hope the stuff that happened with BU in RE7 was just some sort of test and that BU simply becomes a weapons manufacturer in the future that helps both the BSAA and DSO.
With that being said, the irony of the name Umbrella helping out in the fight against biowarfare would actually fit the plot much better. While people may not particularly agree with the name, just the idea of knowing they were simply making guns could actually come to terms with society.
As I said before, having them conducting field missions is unacceptable if people don't fully trust them because combat data can be gathered for them to create B.O.W's or even sell that data to unpleasant parties, Chris of all people should know this.
BU can actually fit the plot, but as a mere firearms manufacturer. "Umbrella once created B.O.W's, now they create firearms to kill them."
Yeah, the militaristic aspect of the series has great attention to detail, mostly with firearms. As I said, I wish they did the same with CQC because it greatly increases your chances of survival when you're unarmed or out of ammo, even against B.O.W's.
For example, Chris killed zombies unarmed in Vendetta, his knife skills were effective against some of the toughest B.O.W's, Joe Baker survived the swamps with his bare fists etc...
I wish they at least made a file once in a while to mention the use of martial arts and hand-to-hand combat. Not only that but I seriously hope they go into more detail when it comes to knives with some special models being produced and how effective they can be against B.O.W's.
In Not a Hero, even with the Albert-01P and Thor's Hammer, Chris still carried a Tactical Knife that apparently was fine tuned just for him. With that we can the see the importance of knives in general, firearms run out of ammo, knives don't.
BU was founded in 2007, but it waited for over five years until the situation got so bad that their help was needed. Right now their abilities to send teams is limited and under BSAA supervision, but they are slowly building up their reputation. The fact their guns are so famous and save lives like Ethan means it's working.
They also have that secret team with 3A7 that steals virus samples and puts on demonstrations for bioterror groups. They are being smart with their rise to power, but it will take time. That's why their role in RE7 was so minor.
BU produced the Brainer axe. It's not a knife, but it is able to destroy a zombie's brain in a single strike. It also has a built in stun rod and can be used to climb over obstacles in the battlefield.