Your hypothetical is not actually far from reality. The Roman legions in western and Northern Europe were facing groups of people who used large, slashing weapons. Not quite battle axes, but think unwieldy two handed swords. This lead to Roman military equipment in these areas being designed to come up against such weapons.

The ‘stereotypical’ Roman legionary comes from Northern Europe clad in a wide brimmed Gaelic helmet, Lorica Segmentata armour that deflected swinging blows, and the scutum would’ve come up against such weapons too.

From the archaeological record we know that the scutum wasn’t a single piece of wood. Instead it was laminated, layers of wood pressed together, making it lightweight but strong. Combined with the curved shape, blows possibly could’ve bounced off a scutum.

We can’t know for sure, there are very few scutums in the archaeological record, the best being preserved at Dura Europos, a city on the Roman-Parthian border. But the technique of making this shield may have been different from that in Europe, however the European climate prevented their preservation. But tombstone reliefs and the presence of shield bosses let us know they were definitely used across a wide area of the empire. From that alone we can conclude that the scutum must have at least been effective in defending its user against a wide variety of weapons, and undeniably strong.

If you want to know more about shields and why the Roman Legions moved away from them I’d recommend: Bishop & Coulston’s Roman Military Equipment: from the Punic wars to the fall of Rome.

I’d also recommend Sim & Kaminski’s Roman Imperial Armour: The production of early imperial armour, on how the Scutum was produced.