I'm going to approach this question in two steps: what metals are you talking about, and could you have a planet where those metals are not easily extractable.
I get the sense that you're specifically referring to the non-lithophile metals, which include the d-block transition metals iron, nickel, copper and gold, and the chalcophile metals zinc, tin, lead, arsenic, mercury and silver.
This is an important distinction, since the advent of metallurgy was a critical step in human development in taking us out of the Stone Age, and it might be reasonable to posit that any advanced civilisation would follow a similar trajectory.
The final phase of the Stone Age, as we transitioned from the Neolithic to the Bronze Age, is called the Chalcolithic because it's marked by the first use of copper (although lead-smelting may have slightly preceded copper-working in some places). The Bronze Age initially alloyed copper with arsenic, but bronze made from copper and tin turned out to be both less toxic and more durable; bronze, in turn, was replaced by superior steel tools. Steel requires a sophisticated ferrous metallurgy involving iron alloys with a carbon content, and knowing how to make it is the mark of a culture's entry into the Iron Age.
[NB: There are plenty of iron relics that predate the Iron Age, but these were made from meteoric iron, an iron-nickel alloy that requires no prior smelting of ores; terrestrial iron's high melting point is well beyond the temperatures that could be achieved in Stone Age pottery kilns.]
Wikipedia describes the early stage of the Earth's formation:
The proto-Earth grew by accretion until its interior was hot enough to melt the heavy, siderophile metals. Having higher densities than the silicates, these metals sank. This so-called iron catastrophe resulted in the separation of a primitive mantle and a (metallic) core only 10 million years after the Earth began to form, producing the layered structure of Earth and setting up the formation of Earth's magnetic field.
If we assume that rocky exoplanets would follow a similar trajectory, we can certainly postulate that the non-lithophile metals (see my first section) would be depleted in the lithophile mantle. However, I'd expect there would still be ore bodies of even the most heavily depleted metals (e.g. iron), due to volcanism or as a relic of the earliest crust before the "iron catastrophe".
The giant impact hypothesis provides one mechanism for an exoplanet to form with a much higher concentration of lithophile elements. It's proposed that a solid object (Theia) crashed into the early Earth, ejecting a significant proportion of the two mantles (mostly lighter lithophile elements) into space. Much of this ejecta ended up forming the Moon. A similar scenario but with one or both bodies more massive could certainly result in an even bigger body than the Moon forming out of this lighter ejecta.
However, it's also suggested that the giant impact not only re-liquified the Earth's mantle but caused significant remixing of the mantle with the outer core. It's not clear to me whether, in the absence of a giant impact, there would have been an even stronger differentiation of elements: in other words, even less residual iron in the mantle.
This is all supposition, of course, and there are many questions still to be answered in the Theia model. Nonetheless, it seems reasonable to say that it is indeed plausible for an exoplanet in the habitable zone to have a significant deficiency of non-lithophile elements in the planet's crust.