"Chemistry might be important"
Conc is nearly all about chemistry. You mention curing rather than drying so you surely have some idea about what is going on. The Romans did not have electron microscopes so could not watch the way the matrix develops around the aggregate etc etc from the get go. To be fair, I fried my first sample in the beam at college by over focussing.
They didn't use rebar because they generally built in compression - arches etc. Rebar and pre-stressing enables members to cope much better under tension. A PS beam or slab is a modern marvel and even protects the steel from fire - bonus.
Cure times: weather/environment. In hot climes you need to stop the water buggering off the surface and leaving cracked and spalling surfaces before it even cures. It may also over heat (exothermic reaction). Cold - slower curing, too cold - no cure and frozen water (total disaster). Underwater - watch your fines wandering off and going for a smoke behind a reef and your structure collapsing, unless you keep them in place.
Concrete curing is not like smoking a joint of meat! A quick or slow cure may be indicated depending on conditions. We have admixtures and all sorts to fiddle with parameters. Then you have things like grading and composing your agg. and other exciting stuff.
I could go on at some length - it is really, really complicated. Roman engineers managed to invent an ancient wonder of chemistry and physics that was concrete. Their approach to its use and improvements was obviously rather better than what passed for science and medicine at the time! They do seem to have experimented and gone with what worked best but it was never deliberately developed from first principles. The self healing thing was probably a happy accident.
A Roman engineer had some rather different design constraints than a modern Civil. For starters, failure could quite legitimately be blamed on the god's displeasure. "When that bridge was commissioned, we made all the correct sacrifices and anyway, you are holding it wrong, I mean walking on it incorrectly".
(sp)