What we know now is that lead’s effects are more pronounced as developmental issues. A little lead exposure as a child can lead to a violent temper. So once children were not born into a low grade cloud of lead contamination, they were set up for fewer mood disturbances as teenagers and young adults. Feeling like violence is your best avenue for conflict resolution leads to crime. So the change wasn’t over night, it was over 20 years.
I expect that whatever effect was going on in Rome if there was one, which seems to be up for debate, counted on pregnant women exposed to lead via alcohol and acidic foods, neither of which young children would normally encounter. Meanwhile lead dust from exhaust got -everywhere-, and paint a lot of places.