It tries to fill vdevs up evenly, so in a clean mirror filling up to full, it does distribute over the two, same as striping.Btrfs/ZFS, as far as I understand it, DO NOT STRIPE. They distribute, which is not the same and does not ensure even writes across the RAID.
Now if you have super weird access patterns that hammers sections of the data file, small enough that it doesn't span both drives, then yes it could write to only one.
In reality, you rarely rewrite existing data unless running databases like Postgres and Postgres runs just fine on ZFS (with compress + recordsize=16kB), distribute and stripe have no performance difference.
Postgres WAL files are append only and don't hammer a single 16kB record. Data files are randomly accessed and written and again, >> 16 kB, so stripe or distribute, they both use all available disks.