Azure supports 50,000 parts, zone-redundancy, and append blobs are supported in the normal "Hot" tier, which is their low-budget mechanical drive storage.
Note that both 10K and 50K parts means that you can use a single blob to store a day's worth of logs and flush every minute (1,440 parts). Conversely, hourly blobs can support flushing every second (3,600 parts). Neither support daily blobs with per-second flushing for a whole day (86,400 parts).
Typical designs involve a per-server log, per hour. So the blob path looks like:
"{account}/{path}/{year}/{month}/{day}/{hour}_{servername}.txt"
This seems insane, but it's not a file system! You don't need to create directories, and you're not supposed to read these using VIM, Notepad, or whatever.The typical workflow is to run a daily consolidation into an indexed columnstore format like Parquet, or send it off to Splunk, Log Analytics, or whatever...