Large shields have been pretty common all over the world in ancient and even later periods of warfare. The Ritsuryō-era Japanese armies used huge mantlets similar to those used by various European medieval armies, which were used lined up or overlapping "like roof tiles" to form a portable wall for archers, though the Japanese never really used hand-held shields much, but the heavily armoured bushi didn't really need them (Friday 89-90). The Achaemenid Persians utilised similar tactics for their infantry, with archers and other troops fighting from behind large shields that were basically set up like a wall (Connolly 23).

The Romans adopted their shield most likely due to influence from other Italian groups, though it was originally oval-shaped and only slowly developed into the rectangular version you're probably familiar with (Keppie 19). The Romans were far from the only group using large shields, and in fact large shields were pretty typical throughout the entire Western Mediterranean (and especially to Italy, including the Samnites, though the Roman version seems to have been heavier (Connolly 95, 107-8). Keep in mind even a large round hoplon-style shield, as was also used in the Early Republican period, could cover a whole man's body if he squatted down (107). The Gauls also carried fairly tall shields sometimes, though they were not as wide as the scutum and were not convex, and so gave them less protection against missiles (113, 120, 175 also Livy 38.21). The Spanish, who also fought in a comparable 'Western Mediterranean' style to the Romans (trademarked by the use of sword, javelins and large shield: see Quesada Sanz 21) also used shields comparable to the scutum in size (151), not to mention the sword (gladius hispaniensis that the Romans eventually adopted from them (though they more often used a curved falcata 150-1).

That's quite a few examples just from the Western Mediterranean (and Persia and Japan) of large shields, though not all full-body sized. Even the scutum was not full-body sized, as the soldier needed to be able to see over the top of the shield to fight and it needed to be light enough to move around to block blows or attack with the boss. The scutum only covered the entire legionary if he squatted behind it. Any larger shield, such as a pavise or mantlet, was designed to be used more like a portable wall than a personal shield, so they're not really the same thing. However large shields that covered most of the body have been common throughout history, and other users more informed on other periods I know little about (like the Medieval period) would probably be able to go into other examples like the use of pavises by missile troops and pikemen in the Medieval period.

We perhaps shouldn't be surprised that large shields are common, as humans have been similarly concerned with protecting themselves in battle throughout history, though different cultures with different styles of warfare did it differently. Even the Gauls of the Mid-Republic, who had a tendency to fight naked on occasion, still brought their oval shields. A shield is perhaps the most important piece of protective equipment a soldier had in the ancient world, and to not have one would put one at a crippling disadvantage against a combatant who did have one, particularly a scutum or scutum-style shield with a boss in the centre to be used as a weapon. The differences in large personal shields between different societies seem to have often been a matter of slight differences, with the scutum only being slightly larger than many other examples from the Western Mediterranean, and not even peculiar to the Romans. So yes, it is by 'coincidence' that the Romans and Han (and many other societies) used large shields, as no matter where or when you were in the ancient world, large shields (of different shapes and sizes) were an excellent piece of defensive equipment suiting a wide variety of fighting styles, whether Roman, Persian, Celtic or Chinese.*

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*Note that the development of new tactics didn't always follow the adoption of new equipment, usually it was the other way around (Quesada Sanz 11).

Sources:

Connolly, Peter. Greece and Rome At War. Barnsley: Frontline Books, 2016 (1981).

Friday, Karl F. Samurai, Warfare and the State in Early Medieval Japan. New York: Routledge, 2004.

Keppie, Lawrence. The Making of the Roman Army; From Republic to Empire. Norman: University of Oklahoma Press, 1998 (1984).

Quesada-Sanz, F. ‘Not So Different: Individual Fighting Techniques and Small Unit Tactics of Roman and Iberian Armies’, in P. Francois, P. Moret, S. Pere-Nogues (eds) L’Hellenisation en mediterranee occidentale au temps des guerres puniqes. Actes du Colloque International de Toulouse, 31 mars-2 avril 2005. Pallas 70 (2006) 1-25.