Well I was thinking culturally mostly, not saying you can point somewhere on a map and say “This is the Roman Empire” - although I might make a case for modern European and American civilization being a distant relative. After all, in America we have our Senate, our Plebes (representatives), and even the official chambers are decorated with Fasces and such. 
Emperor Constantine?
The early church certainly butted heads with Rome, but Christianity eventually became the dominant religion, and tied the church to the government. It was this dominance that allowed them to spread Christianity to pagan Germans, which helped ensure its survival in the west when Rome fell. It was the synthesis of Roman Christianity with the dominant Germanic peoples that formed the foundation of middle age European civilization.
Aside from that, your answer is the same as it always is when asking why someone does something - follow the money.
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M. Mouse,
I remember reading somewhere that a major reason to add a territory or not
occupy a territory was the capacity of that region to support at least one legion
without sucking gold & silver out of the coffers of Rome. Any comment ?
…can’t control Mesopotamia. Persia is a mortal enemy. And some problem with religious zealots in Palestine and Syria. Allied with Arabian Peninsula tribes… who are we talking about here.;)
[nitpick, or not: YMMV]
The Zealots per se were another headache/diplomatic issue for Rome to sort out, along with the Saducees and Pharises, and whatever the hell the Essenes were–but all in 1st century Judea. Ie, before Hadrian, after putting down Bar Kochba with difficulty, and with Rome sick and tired of the Jews after three revolts in one century, put paid to the existence of their political province as a whole and renamed a new geopolitical entity Syria Palestina.
[/nitpick]
Commentary on the Romans from the other end of the pointy stick:
“Auferre trucidare rapere falsis nominibus imperium, atque ubi solitudinem faciunt, pacem appellant.” (“To ravage, to slaughter, to usurp under false titles, they call empire; and where they make a desert, they call it peace.”)
– Calgacus, Caledonian chieftain, 1st Century; quoted by Tacitus in the Agricola.