I think what is true is that minecarts should be one of the last major pieces of infrastructure to go in. The fact is that until you have a fortress that isn't going to be blasted to pieces anytime soon, and isn't going to run out of booze or food quickly, wheelbarrows are quicker and much, much cheaper to produce.
The fact is that minecarts are a large investment requiring a lot of space, knowhow and resources to set up. It's not just the space; it's the designing you have to do, the carving the engravers have to do, and above all designing a structure to power the damn thing if you want it to go up as well as down. This requires engravers, mechanics, carpenters, and architects, and metalworkers if you want metal minecarts, and early on that's time, resources and dwarfpower that is much better used getting defenses, food and an economy going. In essence, the weaknesses of wheelbarrows will not become apparent for rather a long time, because minecarts are investments that will only pay back over a time span of months to years, while wheelbarrows pay off less, but pay off immediately.
That's what I think makes people misuse them. Minecarts cannot and should not be used for one-offs, or if they are you need to have a structural system in place that allows you to create extensions to the system quickly and easily. It is not wise to build a minecart system to empty two veins down to your forges 50 Z-Levels below. It might, however, be wise to plan a system that can be extended to any vein on any Z-Level quickly and cheaply, thus making mining anywhere less of a hassle. Minecarts have to be planned carefully, and the planner must keep in mind that if he wants a good minecart system it will have to pay for itself over the long term; he can very rarely make it pay for itself over the short.