Having a singularly low ability score is fine, so long as you have some high ones to make up for it. This was why 3E had a "minimum value" for characters (which I've rolled and played before). It's not a lot of fun to just be weaker than everyone else.
Back in 1E I played a magic user with a 3 Str and 3 Con, but had an 18 Int and Dex to make up for it. It was part of a bet I made with the DM, who felt that a character like Raistalin would be unplayable. Knowing my limitations, I choose my spells and equipment to mitigate potential disaster. I wasn't a particularly helpful party member, but I survived to about 5 sessions when the DM deliberately murdered my character to avoid losing the bet (I still claim I won).