As noted in the OP, Logistics dictate when, where and how battles and campaigns are planned and often dictates their results.
The importance of Chattanooga was early recognized by Union planners, which dictated the buildup of Nashville as as the Union prime supply base for the invasion of the csa in the West(making it one of, if not The, most heavily defended cities in the CW)
Buells glacial advance from Nashville was the first and early Union attempt to take Chattanooga, in 1862. What slowed Buell was keeping his supply rail line safe from confederate raiders(besides his own cautious nature) In the end, It turned out that the Union Logistics line was more secure running the longer distance through Ky South, than the shorter from Nashville.
The war in the West was a war of Logistics, as noted by the OP, like no other during the War, IMO and not just in Tn but also Mississippi.