Classical Greek atomism arose basically as a response to the Eleatic criticism of the concept of change. The Eleatic argument was basically that if X=Y, then all properties of X must also be properties of Y, but if X is a thing at one time and Y is the same thing at a later time after the thing has changed, then X and Y don't have the same properties, so they aren't the same thing any more. Note that this is an essentialist position: X has an essential identity and it is that essential identity that cannot change.
Aristotle's solution to this problem involved distinguishing between essential and accidental properties. The atomist solution to this problem was to postulate that everything is made up of atoms, so the things of sense perception are aggregates of atoms and have no essential properties of their own. However, the atomists were still essentialists; they just pushed the essential properties down to the atoms. The atoms had essential, never-changing properties and had no parts of their own. However, this is not satisfying, because no matter how small the atoms are, you can always imagine geometrically dividing them up into parts, so the fact that they can't come apart seems more associated with the strength of the force holding them together than to a metaphysical simplicity. "Simple" means having no parts.
Does modern physicalism have the same issue? They can either appeal to subatomic particles as having no parts and having essential unchanging properties, or they can admit the existence of parts. If they think there are base particles with essential unchanging properties, then they are basically saying that science has reached its limit; there are these things in the universe that science is unable to analyze; all it can do is discover how it behaves. If they admit the existence of parts, then they are in danger of an infinite regress of parts of parts. This is a problem for physicalism because the point of physicalism is that the smaller explains the larger. You explain the behavior of a planet by explaining the behavior of the particles that make it up. If there is an infinite regress of parts, then there is no ultimate explanation of anything.
There are various evasions the physicalist can try. They can, for example, say that the basic units of the physical world are not particles but fields, but that really doesn't solve the problem. Are these fields compound objects or simple? If simple, then science has once again reached an arbitrary limit in what it can investigate. If complex, then once again there is the danger of an infinite regress.
My sense is that physicalists would not accept an infinite regress, so they seem to be committed to some layer of the universe that is metaphysically simple, that has essential properties, and that cannot be analyzed further by science.