@DaveE To summarise I will say there is a isolated conductor which has zero E inside and outside. Now it’s charged. For a brief moment there will be a
net internal electric field due to all these charges but that net field will soon disappear because these charges will soon redistribute itself in such a way that the net field on each charge due to all charges is zero. Field at every point become zero. Now the charges are at the surface making perpendicular field to the surface.
Why? Its true that the outside tangential field will have an effect inside tangentially. But that doesn’t mean outside field is perpendicular. The field can well be at an angle and there would be an internal tangential field. Why are we saying because the internal field is zero! Of course It’s will be zero . All the charges are now on surface.
Real reason is that the charges don’t move on the surface. That’s why the field lines are perpendicular to the surface.
I guess it was experimentally seen that charges don’t move on the surface. They become static. That is why we say fields are perpendicular.
@ergospherical You say inside field is zero. Tangential field both inside and thus outside is zero. Field is so perpendicular. But isn’t it possible that there is no field inside but the field due to surface charge is not perpendicular and have a tangential component along the surface.