the sequence signal[s] that the Roman period is one which the BBC apparently now expects its viewers to find instantly recognisable and distinctive, while the pterodactyls do the same job for distant prehistory, the balloons and the steam trains for the long 19th century, and Churchill for the mid-20th. We got ancient Egypt later on, too, but I don't recall anything for any other ancient culture besides those two, any period between antiquity and the 18th century, or of course also anything which might have represented the as-yet-unknown future. That matches pretty exactly with the periods in Earth's history or future which we have and haven't actually visited in other Doctor Who stories over the past couple of seasons, and makes for a useful index of what history means in practice for Moffat-era Who.
Personally, I blame the National Curriculum. At Key Stage 2 (7-11 year olds), the History curriculum requires children to study the following periods: the Romans, Anglo-Saxons and Vikings; Britain and the wider world in Tudor times; and either Victorian Britain or Britain since 1930. In addition, they are required to study ancient Greek culture, and a past non-European society selected from the following: Ancient Egypt, Ancient Sumer, the Assyrian Empire, the Indus Valley, the Maya, Benin, or the Aztecs. In practice, I understand the vast majority choose Ancient Egypt, for which there are many more resources available.
This list is exactly mirrored in Moffat's selection (pterodactyls aside, and adopting the chess player as an honorary Viking/Saxon), with the sole absence of the Greeks and the Tudors - but of course New Who has also made its visits to Elizabethan London. (Have they visited Greece? I don't recall.)
Doing the History Project with lady_schrapnell has borne in on us just how selective children's exposure to history is, at least in school. I particularly regret the absence of the period 1685-1715 from the curriculum. It's hugely important for the modern world, with the Glorious Revolution, the Acts of Settlement and Union, the coming of the Hanoverians, Principia Mathematica, Blenheim and the Treaty of Utrecht, and the modern birth of the Empire... But very little of this is taught to children in school today, at least to Doctor Who's key demographic. The absence of the Middle Ages is rather unsettling, too.
What periods would you like to see more of, either in Who or the classroom?