Probably could add the same flag (leave-root) as rmdirs to the move command. For now you can probably remove that -delete-empty-src-dirs flag and do a second step with:
Maybe I misunderstood what you were asking. but looking at your recent example, you've asked rclone to move test2 to test3. What do you think should have been left behind?.
the one star only matches files in the current directory up the the first slash. the two stars descends into subdirectories. It matches everything forward.
@dell-rob:~$ rclone tree putio
/
├── test2
│ └── file2
├── test3
│ └── file3
└── test4
└── file4
3 directories, 3 files
@dell-rob:~$ rclone move putio putio1 --include=/*/** -vv
2020/06/11 10:09:44 DEBUG : rclone: Version "v1.52.0-001-g1cceadaf-beta" starting with parameters ["rclone" "move" "putio" "putio1" "--include=/*/**" "-vv"]
2020/06/11 10:09:44 DEBUG : Using config file from "/home/xx/.rclone.conf"
2020/06/11 10:09:44 DEBUG : fs cache: renaming cache item "putio" to be canonical "/home/xx/putio"
2020/06/11 10:09:44 DEBUG : fs cache: renaming cache item "putio1" to be canonical "/home/xx/putio1"
2020/06/11 10:09:44 INFO : test3/file3: Moved (server side)
2020/06/11 10:09:44 INFO : test2/file2: Moved (server side)
2020/06/11 10:09:44 DEBUG : Local file system at /home/xx/putio1: Waiting for checks to finish
2020/06/11 10:09:44 DEBUG : Local file system at /home/xx/putio1: Waiting for transfers to finish
2020/06/11 10:09:44 INFO : test4/file4: Moved (server side)
2020/06/11 10:09:44 INFO : There was nothing to transfer
2020/06/11 10:09:44 INFO :
Transferred: 0 / 0 Bytes, -, 0 Bytes/s, ETA -
Checks: 3 / 3, 100%
Renamed: 3
Elapsed time: 0.0s
2020/06/11 10:09:44 DEBUG : 2 go routines active
@dell-rob:~$ rclone tree putio
/
├── test2
├── test3
└── test4
0 directories, 0 files
@dell-rob:~$ rclone tree putio1
/
├── test2
│ └── file2
├── test3
│ └── file3
└── test4
└── file4
3 directories, 3 files
Note though that subdirectories would be left. If you have subdirectories, you'll likely need to run a second command to delete them. or use the --delete-empty-source-dirs and then recreate those directories you need.
THere's also some hacky ways you could do to make it simple for you without running second commands... If you leave a placeholder in the directories then you could run the --delete-empty-source-directories without deleting the folders you care about. Then you'd need to, of course, exclude those placeholder files from moving.
xx@dell-rob:~$ rclone tree putio
/
├── test2
│ ├── dir1
│ │ └── file0
│ └── file2
├── test3
│ └── file3
└── test4
├── dir1
│ └── file6
└── file4
5 directories, 5 files
xx@dell-rob:~$ find putio
putio
putio/test4
putio/test4/dir1
putio/test4/dir1/file6
putio/test4/file4
putio/test4/.placeholder
putio/test2
putio/test2/file2
putio/test2/dir1
putio/test2/dir1/file0
putio/test2/.placeholder
putio/test3
putio/test3/file3
putio/test3/.placeholder
putio/.placeholder
@dell-rob:~$ rclone move putio putio1 --exclude=**/.placeholder -vv --delete-empty-src-dirs
2020/06/11 10:44:56 DEBUG : rclone: Version "v1.52.0-001-g1cceadaf-beta" starting with parameters ["rclone" "move" "putio" "putio1" "--exclude=**/.placeholder" "-vv" "--delete-empty-src-dirs"]
2020/06/11 10:44:56 DEBUG : Using config file from "/home/xx/.rclone.conf"
2020/06/11 10:44:56 DEBUG : fs cache: renaming cache item "putio" to be canonical "/home/xx/putio"
2020/06/11 10:44:56 DEBUG : fs cache: renaming cache item "putio1" to be canonical "/home/xx/putio1"
2020/06/11 10:44:56 INFO : .placeholder: Moved (server side)
2020/06/11 10:44:56 DEBUG : test4/.placeholder: Excluded
2020/06/11 10:44:56 DEBUG : test2/.placeholder: Excluded
2020/06/11 10:44:56 INFO : test2/file2: Moved (server side)
2020/06/11 10:44:56 INFO : test4/file4: Moved (server side)
2020/06/11 10:44:56 INFO : test4/dir1/file6: Moved (server side)
2020/06/11 10:44:56 INFO : test2/dir1/file0: Moved (server side)
2020/06/11 10:44:56 DEBUG : test3/.placeholder: Excluded
2020/06/11 10:44:56 DEBUG : Local file system at /home/xx/putio1: Waiting for checks to finish
2020/06/11 10:44:56 INFO : test3/file3: Moved (server side)
2020/06/11 10:44:56 DEBUG : Local file system at /home/xx/putio1: Waiting for transfers to finish
2020/06/11 10:44:56 DEBUG : test4/dir1: Removing directory
2020/06/11 10:44:56 DEBUG : test4: Removing directory
2020/06/11 10:44:56 DEBUG : test4: Failed to Rmdir: remove /home/xx/putio/test4: directory not empty
2020/06/11 10:44:56 DEBUG : test3: Removing directory
2020/06/11 10:44:56 DEBUG : test3: Failed to Rmdir: remove /home/xx/putio/test3: directory not empty
2020/06/11 10:44:56 DEBUG : test2/dir1: Removing directory
2020/06/11 10:44:56 DEBUG : test2: Removing directory
2020/06/11 10:44:56 DEBUG : test2: Failed to Rmdir: remove /home/xx/putio/test2: directory not empty
2020/06/11 10:44:56 DEBUG : Local file system at /home/xx/putio: failed to delete 3 directories
2020/06/11 10:44:56 DEBUG : Local file system at /home/xx/putio: deleted 2 directories
2020/06/11 10:44:56 INFO : There was nothing to transfer
2020/06/11 10:44:56 INFO :
Transferred: 0 / 0 Bytes, -, 0 Bytes/s, ETA -
Checks: 6 / 6, 100%
Renamed: 6
Elapsed time: 0.0s
2020/06/11 10:44:56 DEBUG : 2 go routines active
@dell-rob:~$ find putio
putio
putio/test4
putio/test4/.placeholder
putio/test2
putio/test2/.placeholder
putio/test3
putio/test3/.placeholder
dell-rob:~$ find putio1
putio1
putio1/test4
putio1/test4/dir1
putio1/test4/dir1/file6
putio1/test4/file4
putio1/test2
putio1/test2/file2
putio1/test2/dir1
putio1/test2/dir1/file0
putio1/test3
putio1/test3/file3
putio1/.placeholder
@dell-rob:~$