Why do large, aromatic residues prefer beta-pleated sheets?
This table is from the Wikipedia page for α-helix:

As you can see aromatics are not the worst offenders. In fact, barring proline (whose backbone torsion angles are unsuited to helices), Gly is the worst offender. A likely reason for this is Gly being too flexible i.e. its small side chain H allows it to adopt backbone torsion angles unsuited for α-helix.
As another example let's look at silk, an extended anti parallel β-sheet structure, from libretexts.

As you can see, the small side chains of Ala and Gly in fact allows the β-strands to come close enough to form backbone hydrogen bonds. In fact, from the same reference I quote - &quot;Unlike the α helix, though, the side chains are squeezed rather close together in a pleated-sheet arrangement. In consequence very bulky side chains make the structure unstable.&quot;
So it is not entirely true that aromatic amino acids prefer pleated β-sheets.
So what are we missing? We are missing the chemical environment in which the the amino acid residues are placed. Remember, most of the propensity charts we look at are average propensities across known protein structures. In a specific protein, its specific chemical context can radically change the secondary structure propensities.