I wonder if it's more useful to think in terms of Limits than individual Attributes.
Pros: this nicely sidesteps the "STR 1 chars can't lift more than a one-year-old" and "LOG 1 chars are too deficient to become shadowrunners" arguments, which I find to be problematic as STR isn't the only Attribute used for lifting and LOG isn't the only Attribute that describes mental acuity
It also works much better with game mechanics. Your BOD: 6, REA: 1, STR 1 human is going to be a big dude who can take some punishment, but doesn't have any raw strength or reflexes to speak of, though he can carry around 10kg without any trouble, and can dead lift up to 120kg if he got really really lucky. On the other hand, his Physical Limit is going to be 3, so no matter how much he tries to learn Kung Fu or how to be a little sneak, he's not going to get very far. I won't even get into Running. If we want to be more realistic about it, we can look at a char who has BOD: 3, REA: 3, STR: 1, Physical Limit: 3. If we compare that to a char who had a 3 in all of those stats, that'd be Physical Limit 4, so yeah STR counts for a lot, but generally when we're talking about how "fit" someone is, or even how "strong" they are we really talking about an interplay of multiple attributes.
Similarly, when we're talking about how smart someone is, we're rarely talking about LOG in the SR sense. A middling LOG, high INT character may be able to "feel" her way to the right solution, but a LOG: 1 INT: 6, WIL: 1 char is going to have a rough go of it. Even with a Professional skill ranking in Perception, she just won't have the fortitude and systematic thinking processes to notice a lot of things that have been hidden -- or to know where to look for them in the first place.
Cons: this leaves AGI out in the cold. Honestly, I'm kind of ok with that. Your weakling gun bunny might be really light on her feet, able to cover long distances elegantly and quickly, and shoot with the best of them, but a low BOD and STR are going to tax her on things that she should rightly be taxed on.
Anyway, don't mean to derail; just my 2¥