The problem with lowering the database compatibility level is that you can’t leverage the new engine functionality available under the latest compatibility level.
This problem was solved in SQL Server 2016 with the introduction of Database Scoped Configurations which gives you the ability to make several database-level configuration changes for properties that were previously configured at the instance-level. In particular, the LEGACY_CARDINALITY_ESTIMATION database scoped configuration allows you to set the cardinality estimation model independent of the database compatibility level.This option allows you to leverage all new functionality provided with compatibility level 130 but still use the legacy CE in the odd chance that the latest CE casuses severe query regressions across your workload.
Each has its own specific use cases, so it’s good to know all three.