Why is the beta-lactam ring essential to the activity of beta-lactam antibiotics?

Because it acts as a rigid hydrophobic anchor that inserts into the cytoplasmic membrane and blocks nutrient transport channels essential for cell viability.

It chelates divalent metal cofactors in autolytic enzymes causing those enzymes to hyperactivate and digest cell wall components independent of PBPs.

It mimics the D-Ala-D-Ala substrate of PBPs, enabling covalent binding and inhibition of the cross-linking enzymes; cleavage of this ring by beta-lactamase abolishes activity.

Because it is the principal determinant of oral bioavailability by protecting the molecule from first-pass hepatic metabolism, explaining why versions without it are rapidly cleared.