A rollup is only as trustworthy as its data. If an operator posts a state root but withholds the underlying transactions, users cannot prove what they own or construct a withdrawal, even though the chain shows a valid-looking root.
Systems that post full data to a layer-1 give the strongest guarantee. Designs that post to a separate committee or external network are cheaper but reintroduce a trust assumption, and they are not equivalent no matter how the marketing reads.
Example: dedicated data space cut rollup costs by an order of magnitude, so a $0.40 L2 swap became a few cents. That cost is passed through, which is why L2 fees still spike when base-layer demand for data spikes.
Related: rollup, layer-2, blockspace, sequencer