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The inertia tensor encodes the mass distribution of a body, so it does depend on the mass, but also on where it is located.

The URDF tutorial you point to states that

"If unsure what to put, the identity matrix is a good default."

I highly disagree with this statement, as there is no one-size-fits-all inertia. In fact, this value will probably be too large for most links used in human-sized robots (or smaller). In my experience, heavier mobile base links (in the 50kg-100kg range) have inertias that fall within this order of magnitude, but almost all other smaller links (belonging to arms, legs, heads) have inertias that are between two and five orders of magnitude smaller.

That being said, this statement is only saying that for a given mass, you're assuming a fictitious mass distribution the yields the identity. Although it may seem unrealistic, it is possible to distribute mass so that a desired matrix results.