You have to bear in mind that BSK was a bit different in tone to the other groups in that it was more about guys with similar ideals and attitudes coming together rather than trying to take over the business or hanging around old buddies. There wasn't an agenda, in fact it was more a creed.
They all got tattoos for a start, which to my knowledge the other groups didn't do and says it's more than buddies looking out for each other... To get something tatted like that is serious. While guys like Brian Lee were among Taker's closest friends (his best man no less) the rest were either guys he knew from USWA or WCW like Charles Wright and Rikishi or guys who came into the E and were somewhat similar to Taker in how they looked at the business and notably also in size a lot of the time. It's kinda like how the Lord of The Rings cast in the Fellowship all got a tat... it's brotherhood.
Of the group probably Savio was the physically smallest but that was not an issue... the rest were all "big, tough, respected guys" who put the business first but knew Taker was "the daddy" so to speak and knew their roles.
They nearly all made their best money working with him in some form and back then as now Taker was calling his spots on who he worked with in a way Shawn couldn't, remember how he was gonna work with Hunter and Kid exclusively when he had the belt? Nah... Taker saw to it Vader got his fair crack, while not one of the crew he was someone Taker respected. Same for Foley.
Someone like Kama made more out of that feud with Taker in 95 than he did as his whole run until the Godfather merch took off. He was there in 91 as Shango remember...
The group likely became more prominent in 96 as a response to 2 things, the Kliq's disbanding/weakening when Nash and Hall went to WCW and Taker's injury at the hands of Mabel.
Until that time Taker was exclusively booked to face giants as an attraction, it was only once that orbital got broken that Vince decided to change tacks with Taker and start putting him into matches with Shawn, Bret and the like.
It's arguable at this time was when he really "learned to wrestle", Taker's two talents were being able to soak up the experience in that years period (cos he was not the revered worker at that point, by 97 he was 10 times better than in 95... and getting guys on side to help his cause and made sure Shawn and Bret did things "the right way" when it came to Taker. It would have been easy for Shawn to pull the Hogan match on Taker in 96/97... or Bret to refuse to lose to him as even without Nash and Hall, Shawn was still a ballache to deal with.
Having diverse guys like Yoko, Savio, Simmons and Crush in your corner will counter any shenanigans Shawn or Bret might try and play as these were their bread and butter guys. They might work Taker once on PPV but the house shows they'd be working guys from the BSK.
Shawn and Hunter would never try f***ing with Taker with those guys in his corner cos they knew they would get hurt, Yoko could drop that leg like a feather or not... Simmons could dismantle them in a second with just a kick (as he did to Ahmed for dissing him) and Juan Rivera was an MMA maestro, not pushed but a hard bastard who could genuinely have hurt them.
So Taker's 2nd great talent was able to draw people to him even in the early stages backstage and by the mid 90's he was the "locker room leader" in the way the Kliq or Bret could never be and while for a period of one year the Kliq ruled the roost, once Nash and Hall were gone the BSK were the true guys in charge... put it this way when the screwjob happened the ONLY guy's reaction Vince was truly worried about was Taker's... had that gone south, Vince might not be where he is today.