Note: I need to try to summarize my earlier replies better, btw.
A lot of universalists do believe this, probably a majority, but I don’t know that it’s a general consensus. I wouldn’t put things that way myself.
I would say the evidence rather points to ‘eonian’ and ‘olam’ primarily referring to God, both as a Jewish euphamism and as a Greek philosophical euphamism, although the term was borrowed from a prior usage of meaning an indistinctly long time (which might or might not mean never-ending but could also mean a few years or even days, olam being a physical metaphor regarding the eastern horizon.)
This multi-variant usage explains the spread of its usage in scripture; and does so in a fashion neutral to the question of ECT vs. anni vs. UR.
It also explains why different exegetical strategies seem to all work pretty well when trying to reduce it down to one meaning (though none of them perhaps perfectly well.) Things get more complicated when related prepositional phrases (like ‘eons of the eons’) are also factored in, as well as more rarely used terms like aidios. (A term which itself could have one or even both of two distinct meanings!)
As the most important meaning would be the affirmation of the never-ending life of God, and (arguably) the next most important meaning would be the hope of the life of a saved person, it would be natural to start simplifying things for ancient evangelism (just as for modern evangelism!), and try to always simplistically read it as never-ending (despite clear scriptural counterexamples to the contrary). Considering that this would just as easily result in a threat of permanent never-ending punishment (of one or another kind), and that there is documented evidence that this was somewhat useful in scaring people into behaving rightly (and even more useful in initial evangelism), the natural tendency would be to read “eonian” (and related) threats that way, too. (A tendency reasonably reinforced by the occasional Biblical habit of using the term to parallel the life and the punishment to come.)
Add to this any tendencies toward using Christianity as a form of Roman state control, and the end result can almost be predicted. (Completely aside from any question of whether sinful people would be more or less inclined to expect no salvation from sins but would be very interested in salvation from punishment.)