Basically: it is your decision
If by "UNIX File System" you mean UFS, then a parent directory inode does not cache the file types, it only contains the files and corresponding inodes. Source: UFS File Systems (PDF, see chap 15.2.2)
This might not be the case for all file systems, it is a design choice. And for your file system it could be your design choice.
For the silliness of this choice, I would disagree. Think how many times would the system have to check for the types of files under a directory? You have to balance the frequency of a
ls -l command with the extra space that caching the information in the inode would take.
If your file system is a cluster-like (e.g. glusterfs) or network-like (e.g. nfs) one, then this could be a good idea due to the possible latency of accessing all the inodes. On local storage this could be less of a concern.
In addition what is your file system trying to achieve? If it is designed to be efficient with directories that contains each thousands of files, then it could be worth considering caching the file types, if it is designed to be lean with the smallest footprint then caching could not be avoided.
Note about ext2, 3 and 4 and the filetype feature
It seems that
ext2-4 can do exactly what you have in mind. It can cache the file types in the directory entry. This is only active with the feature
filetype as filesystem creation time. When this feature is used, then ext4 uses a different structure for the directory entry which can have a cache of the file types. This applies to ext2 and ext3 as well.