Transport of cargo in ships like Enterprise
would actually seem to weigh in favor of having dedicated cargo vessels. While it might work for relatively small volumes of stores or emergency situations to be shipped on a cruiser, problems would come when the vessels' multi-purpose roles conflict. If you need X-cargo at Y-location at Z-time, but it is shipping on a cruiser that is needed for a tactical situation at location-A immediately, that doesn't work.
It has also been real-world experience that military logistics is best handled at a high enough level that it can be prioritized without regard to "local" considerations by individual commanders. The US Transportation Command today is a unified command with full control of its own assets and a four-star commander who answers only to the Secretary of Defense and President. Unless Enterprise
changes chains-of-command for transportation missions, it seems unlikely that vessels like her would be used as transports on anything more than an occasional ad hoc