It does not make sense
In general, it does not make sense for this to work. The foremost reason is that the units of measurement are not standardized in this time period. In the ancient world, the weight (or mass) of currency was rather well known, but that was a result of official dies for pressing coins being taken from one place to another. The roman foot was a recognized and widespread unit of measure; but, there was no universally fixed way to ascertain whether a foot was really a foot. That is, there was no guarantee that a foot as cut in the quarry in North Africa was the same foot the builders were using to line up the marble blocks in Ephesus.
That was not developed until the Scientific Revolution in Europe. Christopher Wren's definition of a meter by the length of a pendulum that took one second to swing was the first start in 1660 and more advanced measures followed. Until there was a standard unit of distance measurement, it was essentially impossible to manufacture standardized parts in remote locations. This isn't a problem so much if you cut all your marble blocks too big; but what if you cut a marble block too small before shipment? If you only only use standardized parts, then you have just wasted that block.
Effective as opposed to theoretical standardization took longer still, until the machine parts makers of the Industrial Revolution (~1790s onwards) started getting demand for accurately machines shafts and gears and dies and what have you.
So, I'd argue that until a scientific revolution allows accurate length measurements, then there is no such thing as "standardized" parts, because the parts cannot be easily standardized.
Long distance shipping to the capital can be done
If you aren't standardizing, then you are just shipping valuable building materials long distances to the capitol. There is plenty evidence of that happening.
- The Romans looted several very large, millenia old obelisks from Egypt that are still there today.
- Rome itself was famous for its many colored marbles, each sourced in a different part of the Empire:
- The Carrarra mines are famous for the pure white marble that many associate with Rome today. In particular, the statue of David is made of Carrarra marble.
- Rosso Antico was a deep red marble from Greece.
- The Chemtou marble quarries were famous as export sites for mass quantities of marble in the later Empire; and also for marbles in "Numidian yellow."
It makes a lot of sense for building materials to be brought from all over an empire to the capital, or the other large cities (like Alexandria, Carthage, Ephesus, and Antioch of the Roman Empire). It doesn't really make sense to build these materials in standardized sizes, because the scientific technology of the time was not enough to ensure that they would fit.