The biggest reason is if you're using Postgres already as an operational database and want some timeseries/analytical capabilities. Originally Timescale wasn't

The biggest reason is if you're using Postgres already as an operational database and want some timeseries/analytical capabilities. Originally Timescale wasn't much more than automatic partitioning but with the new compression and scale out features, along with the automatic aggregations and other utilities, it can actually be pretty good overall performance. It still won't get you the raw speed of Clickhouse but instead you get all the functionality of Postgres (extensions, full SQL support, JSON, etc) and can avoid big ETL jobs. Another PG extension is Citus which does scale-out automatic sharding with distributed nodes but is more generalized than Timescale for handing non-timeseries use-cases. Microsoft offers Citus on Azure.