Cohorts retain good stamina due to their extensive training and drilling. Phalangites do as well though that may have more to do with the way the engine handles them than anything else.
Heavy infantry shouldn't be running around much. They should advance into javelin range, toss their javs, and then begin to exert themselves. In other words, you shouldn't be able to race heavy infantry into position without much penalty. They will still fare very well in the main line but keeping fresh reserves may also be more important. They will in no way be useless

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