I never looked into it really closely but one of the reasons I moved from Prometheus to InfluxDB was Prometheus wants to timestamp observations at time-of-collect, while all my (batch) jobs want to publish an observation with a stated timestamp.
Prometheus metrics exposition format supports user-defined timestamps [1]. There is an alternative time series database - VictoriaMetrics - which supports data ingestion in Influx line protocol, while providing Prometheus querying API with PromQL [2].
Conceptually, the docs I've read for prometheus basically say doing this is "wrong" and even the docs you pointed me at say it's a rare case. My use cases are completely the opposite, so I won't be adopting a system which actively tells me I'm doing it wrong.
