Everybody needs a martial weapon proficiency
The shield bash rules say this (emphasis mine):
You can bash an opponent with a light shield or heavy shield, using it
as an off-hand weapon. See Table: Weapons for the damage dealt by a
shield bash. Used this way, a shield is a martial bludgeoning weapon.
For the purpose of penalties on attack rolls, treat a heavy shield as
a one-handed weapon and a light shield as a light weapon. If you use
your shield as a weapon, you lose its AC bonus until your next action
(usually until the next round). An enhancement bonus on a shield does
not improve the effectiveness of a shield bash made with it, but the
shield can be made into a magic weapon in its own right
Shield proficiency says this:
Benefit You can use a shield and take only the standard penalties.
Normal When you are using a shield with which you are not proficient, you take the shield’s armor check penalty on attack rolls
and on all skill checks that involve moving, including Ride checks.
Shield proficiency doesn't give you any kind of weapon proficiency with shields. It gives you the ability to use the shield and not take the armor check penalty. In order to not take a penalty for using a shield bash, you need that martial weapon proficiency. Classes that give you all martial weapons take care of that pretty easily, like a level of Fighter (or Radiant Servant of Pelor if you're a Cleric).
What about "Simple Weapons Only"?
The other classes you mentioned actually have a list of what they're proficient in, the Cleric's "simple weapons only" is just shorthand for a list that has every single simple weapon on it. It doesn't mean that Shield Proficiency works differently for Clerics than it does for everybody else.
It's also worth noting that the Cleric says "all simple weapons", not "only simple weapons". It's not a special rule or exclusion, it's just a shorter way of saying it than listing every simple weapon.
Pathfinder - The Same
From looking around, this appears to be the same in Pathfinder. The shield bash rules are basically the same, the shield proficiency rules are worded a bit differently but don't affect this, and James Jacobs (Creative Director at Paizo) agrees.
In fact, the Paizo FAQ states clearly that shield proficiency != weapon proficiency with shields.
Best Answer
The rules
The answer is no, there are no shields granting cover on its own and allowing to bash with them. Having such a shield would destroy the balance because tower shields would become obsolete in the face of a shield that does both and heavy shields would be at least challenged, depending on your playstyle. I am also not aware of any official publication that lists a scutum shield.
How to handle a scutum inside the rules
The scutum can be seen as heavy shield. It is lighter than a tower shield and does not provide full cover until you use a tactic like the testudo, that makes use of interlocking those shields and protecting a whole block of soldiers.
The scutum can be seen as a tower shield. It's almost the height of a soldier and should provide cover if used correctly. However, it was never actually intended to be used to bash in the way that D&D defines a shield bash. D&D defines a shield bash as an offensive maneuver in which the shield loses it's protective qualities and instead is used to hurt an enemy. The scene linked in the video is exactly the opposite. The roman soldier uses the full protective capacity of the shield against one enemy while striking for the other. The enemy the shield was used against took no "damage" in D&D terms. Using a shield this way is a very useful combat tactic and certainly shoves a more fragile warrior a few feet, but it is not giving up defense for additional damage. It's not a shield bash as D&D defines it and I doubt that the romans ever taught it to be used the D&D way.
Either way is fine, mechanically. You decide.
Suggestions
There are a few feats for fighters that go in that direction. Phalanx fighting for example. If you wanted to mimic Roman Legionnaires, you could house rule a feat for testudo formation fighting. I think it would fit right in with the other formation fighting feats. Rulewise the shield would be a heavy wooden shield and using testudo formation could grant cover instead of the bonus AC that other shield formation feats grant.