Or perhaps Socrates thinks that happiness consists purely in 'truth and understanding and the perfection of one's soul' - where the key point is just that these are internal goods of the soul, not external goods, so that wisdom is all that is needed to guarantee achievement of these goods. In fact, if we do not know how to use our assets, we are worse off if we have more, for that will make us more active and so more likely to harm ourselves. If this is so, then wisdom is in fact the only thing that it is good 'all by itself'. Step 2 seems to say that wisdom is a necessary component of every good - every other good is good only on the condition that it is combined with wisdom. This does seem to be his conclusion.
Nothing tastes good without salt.
The idea that wisdom is the only good certainly seems extreme. This would be the idea that Wisdom is actually Identical with Happiness. Indeed, it seems to imply that wisdom is a good even if it is never used. But that seems to contradict one of the assumptions of the second argument. Again, if he really means that being happy just is being wise, and there is no more to happiness than that, it seems to imply that, so long as they are equally wise, then one person cannot be better off than another even if one of them is imprisoned in a concentration camp and tortured and the other is a philosopher-king.