If I understand correctly, you propose Romans used the term cohort to refer to army detachments of their Italian Allies, and, from this assumption you conclude that when they used the term cohort it must refer to an Army Detachment of Italian Allies. This is a bit circular.
The Romans used the term Ala to refer to a Legion size contingent of Italian Allies. In the particular examples cited above, maybe the army detachments referenced were Allied Army detachments (though the record is unclear). However, even if in these particular instances the particular detachments cited were Allied detachments, it does not follow that the term cohort was exclusively used in reference to Allied detachments.
The instances you cite tell us that during the period Roman Generals found instances where they needed to detach substantial number of men from the main group. They had to create "army detachments". The instances you cite also tell us that they used the term cohort at least in reference to Allied army detachments. This begs the question: what would they call an army detachment consisting of several hundred Roman legionaries?
My point is that: (1) The term was in use before 100 B.C. when the Marian Reforms took place. (2) The term stood for a formation of several hundred men. (3) Rome manned armies of thousands of men for a long time prior to Marius. (4) During this period Rome must have found plenty instances in which they needed army detachments of a size between a maniple and a legion. (5) We know of no other term available for a formation of several hundred men. (6) If a culture has developed a concept, and, attached a name to that concept, if it has a need to communicate that concept, and it has no other word available for that concept, it will most likely use that word to represent that concept.
I already provided evidence of #1 and #2. #3 is a well documented fact.
Maybe we disagree on #4. Maybe you think Romans would never consider operating army detachments of intermediate size, even when tactical conditions demanded it - not even to guard camp, a baggage train, or a river crossing. And, not even when necessary to disperse a unit to gather food, etc.
We seem to agree in #5.
And, we again disagree in #6.
I will agree we don't agree.
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