Some types of L2, like roll-ups, settle to L1 every block.
The "whole point" of L2 is to reduce the amount of resources used to settle its transactions on L1. Some L2s, like Lightning Network, achieve this by settling infrequently. But other L2s, like roll-ups, achieve it by batching transactions in clever ways so that less L1 resources are used on a per-transaction basis.
LN's shortcomings are not issues for zkrollups on Ethereum. Transactions are stored on chain, just in compressed form. A contract checks the validity of all transactions before storing them. The proofs are expensive to generate, but so cheap to verify that a contract can do it on chain.
If your L2 has the same security and decentralization of the L1, then it's another L1. Since it has the performance part of things, it can only have either security (but then it's centralized, so it could fully securely write bullshit, which then gets written to L1), or decentralization (and then you get to write unsecure bullshit, which has no reason to either be trusted or true, and you can write that to your L1).
It could write to L1 immediately, but your writes can still not be trusted or right.
The trilemma is not a law of mathematics with binary outcomes. It's an attempt to describe certain tensions inherent in building blockchains. A great deal of work as been done on Ethereum to balance these tensions. Rollups increase throughput because they move execution off L1, while requiring proof on L1 that L2 executed correctly.
