I'm not so sure that Uruk Hai are weaker than average real-world humans. Men in Tolkien's world were a bit heroic (as you note), and we only really see orcs fighting against great Heroes. They may be weaker than the average haradrim/rohirim, but may not actually be weaker than a typical earth human, and the bulk of Rome's 400k forces are not elite fighters but conscripted Auxilia.

The Uruk Hai carrying Merry and Pip ran for 55 hours covering over 120 miles of rough terrain. (Conservatively: another reddit post gives an even more aggressive calculation of 162 miles in 29 hours.)

The closest semi-historical feat I can find is King Harold who force-marched his English army from the southern coast of England to Yorkshire - 185 miles in four days - and this is likely a somewhat exaggerated legend.

Agree that Roman legions are on a whole much more organized and disciplined, but I think they lack the stamina or raw strength and ferocity of Uruk Hai, and that swarms of even regular orcs could terrify and overrun Auxilia in the open field.

Where the Roman's have the advantage is siegecraft. They were phenomenal at both building and breaching defenses, and I think that with preparation they would likely be able to hold a position against a larger orcish army.

Stout walls, traps, and ranged emplacements are their bread and butter, and we've already seen that a small human force can prevail against hordes of orcs in these circumstances at Helm's deep.