This is IMO, but I think Socrates tried to convey the dangers of being what Sun Tzu termed "haughty" which is synonymous with arrogance and un-necessary confidence.
The idea of being continually filled with doubt in the most extreme way is definitely going overboard IMO.
The sweet spot is knowing to stand up for what you think but also be able to know when you are out of your depth, over confident, completely arrogant, and don't know when to seek the wisdom and judgement of another.
The truth is that no one can possible know everything in their own limited experience, but they can definitely become a lot wiser if they just shutup and listen to people opinions whether they have any amount of truth at all in them.
It's our hard task of trying to sift truth from fiction, and in the process we will come across everything in all forms that have mixtures of truth and fiction, and knowing how to decide the truths usually comes from trying to expand awareness by looking not only at our own experiences, but the experiences of others in a way that is unbiased and where some suspension of disbelief is required to even consider at least initially what another person has said is true.
Recall that in basic logic 101 (Usually taught in 1st year mathematics courses in the form of Discrete Mathematics), one of the most powerful ways to prove something is to assume that it's true and then find a contradiction.
Psychologically this distinction is very subtle, because it forces the arguer to suspend their disbelief and accept at least initially that it is potentially true. In mathematics, we attain a level of truth within the boundaries of the system using this method time and time again.
To be filled with absolute and immense doubt would be a psychological nightmare for anyone including someone like a philosopher, and it's just going to be rife with problems to think that we know and will always know regardless of any experience absolutely nothing.