The romans controlled the Caucasus already more than they controlled Armenia since the 1st century AD.
Iberia was a roman client state. More than Armenia. Armenia was more often ruled by a parthian client king who was just enthroned by the roman emperor. A pretty lousy deal with the parthians.
Provincializing Iberia, Albania and Colchis would have been less beneficial than controlling it via client kings. So the romans did not provincialize the Caucasus by very good reasons. Also the Caspian Sea was not beneficial for the romans. Not by strategic reasons, because there was no partian province worth an attack beyond the Caspian Sea. And also not for trade with China. The Parthians never blocked or overtaxed the trade with India or China. Even not during war-times. The parthians were not suicidal or complete morons. And even IF the parthians would have blocked all trade with India and China, THIS would have been HIGHLY
benficial for the roman economy!!! Unfortunately, they never did it
So finally, the roman control over the Caucasus via client kingdoms was the best solution ever possible. A more intense control of Armenia would have been desirable. But Armenia was a bit challenging from a diplomatic point of view.
And do never forget: the foreign trade balance of the Roman Empire with India and China was negative and basically detrimental for the roman economy and contributed to the Fall of Rome. Everything which is able to reduce the volume of this trade should be very welcome. And everything able to increase or ease this trade
should be avoided BY ALL MEANS!!!
PS: Just if you are not
G.A.Washington who invented a "Roman India Company" owning indian farms and therefore keeping the profits and the roman silver inside of the empire.
https://www.alternatehistory.com/forum/threads/on-eastern-shores-–-a-roman-timeline.392038/