We do exactly this!
Our startup Opsian (https://www.opsian.com) is a very low overhead continuous profiling service for the JVM.
Our JVM agent sends profiling data from your instances to our cloud environment where it's indexed, aggregated and made available for hotspots/tree/flamegraph reports.
We even have a dedicated report telling you where regressions happen between releases.
(We're actually out at Devoxx 2018 right now doing a talk on why everyone should be doing continuous profiling)