Lots of reasons. Often times the Romans would make a conquered territory a "client state." A client state was a kingdom that did not have sovereignty, so that the inhabitants were still subject to the king's rule, but the king was subject to a Roman noble such as Julius Caesar or, later, the Roman Emperor. In these cases it, leaving the kingdom to be ruled by Rome was not such a crazy thing as the kingdom in question would have already been indirectly ruled by Romans for some time.

The reasons were various. If there was a lack of a successor or if there was political instability in the kingdom, it sometimes made sense to leave the kingdom to be ruled by Rome. A notable example is Pergamon, which was granted to Rome by Attalus III. There had already been a precedence to call Rome to assist in Pergamene conflicts, so Attalus was merely taking precedent one step further in order to prevent one Aristonicus, a bitter political rival, from gaining any power in the ensuing power gap.

Sources: Plutarch
The Hellenistic World and the Coming of Rome, Erich Gruen

If I may expand this question, why did rulers of many cultures do this? I recall that Boudicca's husband did this as well.

If I may piggy back off of this, were they coerced?

Could someone qualified discuss the applicability of the stranger king theory?