A few points:

• Learning for the sake of knowledge is not necessarily re-inventing. How many frogs have been dissected? Surely documentation provides ample detail as to what one will find inside a frog's body cavity. There is merit in this form of re-invention: Experience.
• Reinventing the Good Year Eagle LS-2 tire all over again for any reason aside from educational value would be stupid. But standing on the shoulders of the Good Year Eagle LS-2, tearing into it, educating oneself all about it, and redesigning it with "Run on Flat" technology would add value. If your goal is to create a tool that satisfies a need not addressed in existing tools, you're not re-inventing, you are inventing incrementally with the benefit of a solid understanding of "prior art."
• There are many other reasons for reinventing. But there are many pitfalls too. The oft (overly) repeated mantra of "don't reinvent the wheel" assumes that the inventor hasn't any compelling reason to reinvent aside from the ignorance of being unaware of the availability of a suitable wheel.

When re-inventing, either learn something by doing, prove something thought impossible, innovate something as yet unavailable, or refine something that needed improvement. Presumably in such instances enough thought goes into the final product that it has value-added over the existing solutions. In those cases you're really not re-inventing, you're developing.

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