One might similarly ask if you read what you quoted. What weapon in the PHB is similar to a shield? A shield is strapped to your arm, reducing the momentum you can generate on a swing, as well as limiting the angle you can use it in fighting. There is no weapon in the PHB shaped like it, or used like it - not even remotely.
Further, if there was an intention for it to be used as a weapon, it would be a pretty massive oversight not to list it. It seems pretty clear that the intention was not to allow it to be used as a weapon with proficiency bonus, or do more than d4 damage, without some additional ability.
DMs can rule anything they want, of course, but there is no basis to assume that the shield was intended to be allowed to be used with proficiency, or to deal more damage than any other basic improvised weapon (d4).