I would say what you are seeing is expected, possibly even better than expected. The performance of outputting data depends on many factors ranging from the size and structure of the data itself to the throughput and latency of the storage tier.
Many ArcGIS geoprocessing tools stream outputs to "disk" as they are generated/created, which makes sense because creating the output completely in memory before outputting it to disk isn't doable for many datasets. Streaming outputs to disk continually results in smaller increments but more frequent disk activity. Given that wide-area networks tend to operate on 10s or 100s of milliseconds of latency, and local disks tend to operate with substantially higher throughput and < 1 millisecond latency; it is expected that outputting geoprocessing tools straight to a cloud environment will be slow when the machine doing the processing is not in the cloud.
I would suggest either running the analyses locally and copying just the final products to the cloud environment at the end, and/or process more of your intermediate datasets in-memory (if possible) before copying the final results to a cloud environment.
Also, you could spin up ArcGIS on a cloud-based virtual desktop and do the processing and exporting completely within the cloud.
