But I'm coming from the experience of one of my most-loved characters-and one of my buddy's most-loved characters-both had Logic 1 and Intuition 4. (It's a long story.) Their low Logics played in heavily to their characters(and a 1 is not mentally handicapped, as you have flaws that cause that kind of thing-it's low, but the people can still write and spell, in our games anyway-but don't ask them to do big math.
Under that rule, these characters couldn't have been, and we'd have been out two of our favorites(not only of us, but of people who have seen these characters as well.) By harshly limiting certain things, people can lose out. Which again why I'm a big fan of ''watch the die pools.''

I can see these kinds of characters being acceptable, so long as you had a decent Charisma and Willpower. Stats like, Cha 3, Int 4, Log 1, Will 3 are pretty good and lend towards an interesting personality for the character. Like I said before though, our group considered the minimum of 5 and I was on board with that, but the majority wanted 6 to be the minimum. So that's what we ran with. Since we'll have a new group though, I'll give 'em a call and maybe they'll think 5 is acceptable. If that's the case, I see no problem with dropping it to 5.
My only issue with "watch the dice pools" is that people can have very different opinions about what an acceptable dice pool is. After talking to the Troll's wife, who he taught to play, she was under the impression that any pool under 12 was going to get her killed, and that she couldn't survive a game without at least 3 IP's and that without at least 3 IP's she'd be bored out of her mind, while sitting around and waiting for her turn.
By the way, I don't necessarily think there is anything wrong with saying only 1 stat can be at 1. I actually find that quite ok. But when you start forcing minimums, that, IMO, takes chargen out of the player's hands, which isn't a good thing. (BTW, problem players should be dealt with individually, and not by sticking the entire group, IME.)
I think that a well-written set of house rules, or a style sheet as we call it, you can describe to new players how your group likes to play and what kinds of characters they like to use without just shooting down their concepts straight out of the gate. It allows them decide whether or not they want to play without making a character and sitting down, just to find out that their play style really doesn't match your group's. And I agree that problem players should be handled individually, but some things can be prevented if you give them a hard set of rules to go by. It shows them that it's nothing personal, that's just how you guys roll.
As far as I would go in forcing a minimum, if i absolutely, no holds barred HAD to force it, I'd keep it at 2, since that's generally seen as simply unexceptional and dead average. Again, with only 150 BP to spend on Attributes(that's not even enough for a 3 down the line for a human), something is just not sitting right with that.
Are you saying that even the most spectacular individuals or concepts aren't average at at least one or two things? When it comes down to it, we're all only metahuman. That's why Technological or Magical Augmentation is so advantageous to have. If you're not one of the lucky ones that are born with that mystical spark, then you've got options. Then again, if you're not Awakened and you're not too keen on 'wares, or it's not available because you just can't afford it(though you can always take out a loan with someone, careful who you pick), there's always the old fashioned way of working hard at it and developing the skills to compensate. Swordsmen that weren't strong could always fall back on their swordsmanship, which they worked at for years. Then there's the non-augmention gear out there. So you don't have the best hand-eye coordination, but you have a smart-linked Ares Alpha calculating the effectiveness of suppressive fire for you, in real-time.
Glad the contact thing went well, though. 

We're actually considering a sort of good cookie system for some of the contentious points of the house rules. Something along the lines of, "Yes, 8 BP is the minimum, but if you put in 12 BP you earn the title 'Connected' and get a bonus to your Street Cred." Or something of that kind. Same goes with availability. "Yes, 12F in the max, but if you keep it to 8F you get the title 'MacGyver' and are able to spend an Edge to gain the Jury-Rigger quality for a scene." You know, enough to have fun and encourage people, but not overpower the game.
These kinds of bonuses would only be granted for CharGen, not the milestones of character improvement. I give each PC one story-based good cookie for campaign; a unique enchantment for an Awakened character, a rare piece of cyberware the a street sam, or some such reward for good RP.