In the File System Editor under the Web Setup project I have

witch says that my Sripts folder should have Write Access … but once installed I do not have the user IIS_USR/IIS_WPG (Anonymous User or/and Worker Process) in that folder, and for such, no write access to that folder when used from a hosted level.
This is what I get:

but I should have this:

AllowWriteAccess is used by IIS Web Properties dialog. It’s not used to set permissions on the actual folder on disk. Your folder will use default permissions when installed.
To set custom permissions you can try using XCACLS.EXE as a custom action.