Rome's expansion over Latium was political before it was religious, and the religious consequences went in more than one direction.
Some cults were moved. The practice known as evocatio, calling a defeated town's protecting deity out and offering it a home in Rome, is recorded for Juno of Veii and appears to have been a formal procedure rather than a metaphor, complete with a vowed temple on the Roman side. Others were absorbed by making the Roman state the sponsor of a rite that had belonged to a league of towns, which is what happened on the Alban Mount.
A third group was left in place and simply visited. Nemi kept its own priest, and the peculiar rule attached to that office, that the priest held it until killed in single combat by his successor, was already an antiquarian curiosity to Roman writers. Its later fame is disproportionate to its importance: James Frazer built The Golden Bough on it in the late nineteenth century and made a small Italian shrine into the hinge of a global theory of religion that specialists no longer accept in that form.
What Latium therefore offers is a controlled comparison. The same religious culture is visible at the level of a small town, a league of towns and an imperial capital, in the same landscape, over roughly a thousand years, which is a rare thing to be able to watch anywhere.