Why Rollup? The Triangle of Cost / Speed / Composability System Design
Think of #L1 as the 'Supreme Court' and #Rollup as the 'Fast Review Court'. Large transactions are first sorted and packed by the Sequencer on L2, then 'evidence + results' are written back to Bitcoin to achieve finality: using L2 for efficiency, using L1 for security. This is the original design intention of Bitlayer.
1) Why do costs decrease and speeds increase?
Costs: L2 aggregates multiple transactions into a batch, paying L1's settlement costs once, effectively 'spreading' fixed costs over multiple transactions, thus reducing per capita transaction fees.
Speed: Block creation and execution on L2 are completed at the second layer, TPS and confirmation times benefit from a lighter consensus burden; finality is still provided by L1 verifying batches and proofs.