See, my problem with that is that its a slippery slope. We started out with "only 20BP plus enemies need to be approved by the whole group". Now evil twin is added into the mix. In the game I'm currently in one of the characters is searching for her missing relative. We found him almost immediately, sort of. He left his quiet corp life and is now a psychotic Yakuza assassin. So her 5BP quality now has the chance to become a BBG if its handled wrong.
I'd actually go farther to the other extreme and say that every character should be interesting enough to justify an important subplot. It may not be something that's reflected in Qualities necessarily but I prefer teams where everyone has a life outside of the run. Ideally, when the party is seperate between runs and the GM starts off with "what are you doing" they'd all have something to be pursuing on their own.
As for Enemies in particular, there are a ton of ways for a high BP Enemy (greater than 10) to mess with the character without sending elite snipers after the party. A lot of it involves the GM and the player working together to come up with something that can fit in the game. Here's a couple of off the cuff examples:
The Bad Way
Enemy: Knight Errant. (Connection 6, 1000+ members, National Influence, Limited Magic, Broad Matrix Resources), base value 21
Frequency: 4
The character is a cop killer. In some previous run he was not only involved in taking out a KE SWAT team, he once personally shot a cop on an unrelated stakeout in the face and stole his cruiser. He's SINless and lives in Redmond so on a day to day basis KE isn't going to find him even if they look. On the other hand, he's one of Seattle's most wanted. If he passes the line of sight of a police vehicle at a distance of a block or less or has his picture sent as part of a 911 call, they will come out in force with E-SWAT and they won't be trying to take prisoners. This is the kind of thing that can get an entire party wiped off the face of the earth and also the kind of runner no Fixer or Johnson will touch unless they're desperate.
Same idea, take 2
Exactly the same enemy stats as above. The character used to be a member of Knight Errant. He worked for one of their less publicized divisions and was exposed to some very embarrassing dirt over the years. He quit the company over issues of conscience. While he has no way to prove the things he knows, the split was less than amicable. No less than Damian Knight himself was unhappy with the character storming into his office, slapping down his resignation and disappearing into the night. KE wants to know some of the details of what he knows and why he left. They've already burned his SIN and would very much like to take him in for interrogation. The Knights don't particularly care for someone who turns on his own, especially someone who goes over to the side of the crooks. On the other hand, some people in the company know where to find the proof he needs. They're not above dangling that carrot and calling off the dogs for a bit if he does a "small favor" in return. In the meantime their dragnet will be keeping his contacts constantly on edge. They'll occasionally get a lucky break and intercept the gear he had on order. And if a squad car ever finds him alone in a dark alley, he's likely to wake up cuffed to a KE hospital bed. They could care less about who he's working with unless those people also seem to be in on his dirty little secrets.
If the character ever gets arrested he's not out of the game. He hangs out with Shadowrunners, after all. They just get an exciting jailbreak session intercut with him being interrogated. If he ever makes peace with the Knights, it'll invariably come at the cost of pissing off someone else. Lone Star comes to mind, as does a cell within Ares.