I personally don't like 1's on my own characters, but its more for RP reasons than anything else. I can live with a few 2's.
Mechanically, a 1 means that you are bad enough in that particular area that unless you have training (i.e. some skill points) you automatically fail at anything that is hard enough to require a skill roll. Now, there are people around out there that will tell you a 1 logic means you are a drooling idiot that has to be lead around on a chain and pointed at the badguys. I don't believe this is the case. And one low score doesn't mean that other areas are low. If you have a 1 logic you can still be very personable and charming (high chr) very perceptive (high intuition) and focused (high willpower). But when it comes to abstract reasoning, academics, and memory, you are just plain horrible. Math beyond basic arithmetic is a mystery. Pretty much anything beyond social media and send a text on a computer is not going to happen. Tools? Put them down chummer and back away slowly.
I think worse is the 1 charisma character. If you dump charisma you MUST put a few points into at least etiquette or you are a disaster waiting to happen. I personally like to have a pool of at least 4 in etiquette, as you can buy one hit and I take this to mean you have rudimentary social graces, you know, eat with a knife and fork, not to call the yakuza member offering you the job "squinty", and you can recognize when to shut up and let other people talk, with is often half the battle. 1 chr and no skills basically means that if there is any chance that you will offend, stand out, anger someone, or get the worst possible price on something, you will.