Each additional chain multiplies your attack surface. The contract may behave identically on each chain, but the execution environment does not: gas semantics differ, bridge assumptions introduce trust dependencies, and sequencer behavior on L2s creates timing risks that do not exist on mainnet.
If you need multi-chain presence at launch, deploy on your primary chain first, prove stability, then expand. Each deployment should be independently audited in its target environment, not assumed safe because it worked elsewhere. Bridge-related risk is one of the most common sources of cross-chain losses, and it is entirely avoidable by sequencing your rollout.