I'll admit I'm no typeface expert, but this seems to miss the point. Wikipedia's own page on Roman type [0] says "Roman type was modelled from a European scribal manuscript style of the 15th century, based on the pairing of inscriptional capitals used in ancient Rome with Carolingian minuscules". And visually, there's clearly an influence, though many centuries removed. My point is merely these very old typefaces remain modern looking because we still use similar ones today.
The capital letters were indeed inspired by Roman monumental inscriptions. But all the lower case forms were taken from Carolingian designs. Humanists wanted to copy Roman forms to go back to what they saw as writing uncontaminated with medieval influence, but the texts of Roman authors they used to do so were not actually written by Romans but copied by Carolingian-era scribes. It's why its generally much easier for us to read ninth-century texts than, say, earlier (e.g., Merovingian chancery script, yikes) and later scribal hands (e.g., late medieval Gothic).
"If my grandmother had wheels, she could have been a bicycle." Serif type is based on the use of chisels to carve rock. ANY other semblance is purely speculative. The trademark for Times New Roman is owned by the British, not the Italians.
[0] https://en.wikipedia.org/wiki/Roman_type