First, to imagine "individual electrons" as having well-defined values of $\vec p$ is in no way necessary. The electrons collectively occupy the whole band – which may be described as a subspace of the one-electron Hilbert space. But this subspace of the Hilbert space may be described by many different bases. For any basis, one may say that 1 electron is created into each basis vector. The basis of momentum $\vec p$ eigenstates is just one (although natural) possibility among infinitely many.

Second, more importantly, there is absolutely no sense in which the sentence

This is in sharp contrast to the strong tendency in xyz space for particle wave functions to form compact, particle-like wave packets centered around the last location at which they were "observed."

is correct. The wave functions in no way want to clump. On the contrary, they typically evolve so that they get diluted in the whole space that is available.

Also, the wave function for the momentum $\vec p$ eigenstates has $\Delta \vec p=0$, and by the uncertainty principle $\Delta x \cdot \Delta p \geq \hbar/2$, it unavoidably follows that $\Delta x = \infty$. The wave function of a momentum eigenstate is unavoidably spread in the whole space. In fact, it must have the same probability for the electron to be at any point of the space (well, inside the material).

Electrons are detected at particular points. But the correct explanation of this fact isn't the assumption that wave functions want to get clumped. They don't want to clump at all. The correct explanation, as undergraduate students of physics learn already in the first lectures of quantum mechanics, is that the (squared absolute value of the) wave function describes the probability density that the electron will be found in the vicinity of a given point.

This point is no detail. It's a totally fundamental fact about the wave function and it's also what Max Born got his well-deserved Nobel prize for. It makes absolutely no sense to use the term "wave function" if the speaker doesn't understand that its squared absolute value is interpreted as the probability density.

Even if the wave function for an electron is absolutely delocalized and uniformly covers the whole 1-ton metallic object, the measurement of the electron's position will produce a sharp number. The role of the wave function is that we may predict where the electron is more likely or less likely to be detected. If the wave function is uniform in the whole metal (up to the phase), and it is in the case of a momentum eigenstate, it means that the probability to detect the electron at any point of the metal is the same.

But the wave function doesn't describe the shape (i.e. some internal property) of the electron. The electron is point-like (even in the Standard Model; one needs to go to string theory to revise this assumption). Instead, the wave function probabilistically describes the location of the point-like electron (i.e. an external property). To describe the internal properties of a particle, e.g. a hydrogen atom, one needs a wave function that depends on at least two vectors $\vec r_1,\vec r_2$, i.e. the positions of the nucleus and an electron (or, equivalently, the position of the center-of-mass and the relative position of the electron relatively to the nucleus).