The only bad side of 1 ST is you can't loot corpses of NPCs/unlucky wastelanders/friends. Also you can't loot metal armors in NCR.
You may forget about metal armors at all. Still I can use BA+plasma/laser and carry MFCs, it's not a problem, 18 carry weight is more than enough, you can even stand in NCR and when someone will try to plant dynamite into you, he wouldn't do that because of your overweight, this is one of the funniest momments to observe.
There's also an alternative, if you really want to talk to merchants, is to get 7 IN instead of 6 and 1 CH, get FA and doc to Doc3 prof and craft mentats, mentats will give you +2 CH for 30 minutes, you may simply eat them and live on them and become mentatoniac. It'll save you a SPECIAL point, because you'll spend +1 on IN instead of +2 on CH, but it's only if you're going to increase FA+Doc.
Also... you still can have 6 IN, but you'll need to take... Night Person trait, and get Doc3 prof at night +mentats, so you'll meet IN requirements.
Also don't forget that you can buy nukacola for 100 caps at JT, it's +1 to AG for 30 minutes, it means, if you're not going to use buffout, which lowers AG by 1, you need to take 7 or 9 AG, so with nuka it'll be 8/10.
Good Natured not only for doctors, it's for characters, who aren't going to use more than 1 combat skill, as I see, you're not hybrid of some strange combat styles, you're just SG-user, so Good Natured will give you more SP than take.
Also 1 ST will allow you to use Jet without it's bad side except for lowering DR. Because 1 ST -2 ST = 1 ST anyway. You may get 12 AP, if you'll have 9 AG +nukacola and on Jet. So you'll be able to shoot twice in the eyes from .223 pistol.