Kurt T. You definitely can do that via an exporter - here is an in memory example (https://github.com/open-telemetry/opentelemetry-python/blob/main/opentelemetry-sdk/src/opentelemetry/sdk/trace/export/in_memory_span_exporter.py) - though I have not tried this myself, you could definitely save off the traces as you see fit (e.x. export to phoenix and to disc)
It's worth noting that the Arize platform also supports these traces so if you are looking for a SAAS platform to persist your telemetry data, that's an option too.
