You can still do better by not doing any TSC to nanosecond conversion. Instead, you inject clock adjustments into your log stream allowing you to convert when you decode the logs rather than when you generate the logs.

Using the final version, you would just make the cache refresh() function emit the clock adjustment log entry instead of actually caching anything. Then, any later log entry TSC would implicitly be relative to that clock adjustment log entry when you decode the log. Worst case you would need to persist every clock adjustment entry even when sampling, but that would still only be on the order of a few KB/s at worst and you could still drop entrys with no non-clock adjustment entrys between them.

I can beat this by not trying to wrap a trace span around something that only takes 100ns.

If the thing of interest just runs on the CPU briefly, tracing is not what you want. You want a profiler that only runs when you're looking at it. Distributed tracing is for things that can go wrong and take uncertain amounts of time.