Minimum wage went to a spoon of salt too, don't forget that.
Plus men started wearing robes like women, and worshipped a man who had long hair, confusing children and causing the populace to stop buying mead and thus collapsing the market economy.
Certainly it had to do with cultural cohesion. Part of that being language though I grant that the empire was quite large and had diverse languages in different provinces. The Roman decline ultimately was a failure to be able to secure its borders militarily from mass invasions, so there are correlations to today. All of the other things existed in the empire though what degree they contributed to its decline is difficult to ascertain. To say it has nothing to do with them isn’t any more right than saying it was a prime cause.