To give you a real answer, from someone who loves WebDAV and has written a WebDAV server with an S3 backend, object storage is easier/possible to run at scale and serves a different purpose.
Object storage is and always has been based on a key-value model. You put a key and value in, and later you can request that key to get that value. It technically has no concept of hierarchy. WebDAV supports so much more than that. WebDAV has collections (hierarchy), live and dead properties (S3 has something similar to these), methods like MOVE and PROPFIND, and a system of hierarchical locking (depth 1 locking on a collection and depth infinity locking on an entire namespace).
This means that in order to build a WebDAV server, you need to know a lot of information about what exists in the data storage. S3 is a lot “dumber” in that regard. The funny thing is S3 has added so much functionality that they’ve essentially rewritten WebDAV in a more convoluted form. Whereas on WebDAV you can just propfind a collection with depth 1, on S3 you need to list keys with a prefix and delimiter, then make additional requests for any other props you may need.
Unfortunately, the one thing WebDAV is missing that users of S3 often need is the concept of partial listing. In S3, when you list keys, you tell it how many keys you want back, then it will only give you that many keys max. If there are more keys that it didn’t give you, it will tell you the results are truncated and give you a continuation token. You can use this token in your next request to continue listing keys.
This is where the “at scale” thing comes in. If you have hundreds of millions of keys in a bucket, getting them all back at once would certainly break your system, and probably would tax the server unnecessarily. So basically the answer is S3 is designed for scale.
That being said, S3 is not really designed for humans to interact with. This is where the “different purpose” thing comes in. It doesn’t have a real concept of hierarchy, just common prefixes and delimiters. So something like renaming a directory would require copying every object with that prefix to a new key, then deleting the originals (which is what my S3 adapter does for my WebDAV server). S3 is more meant to be used with something like UUIDs or hashes for keys. Keys that don’t change. WebDAV is designed more like a file system.
I hope that explains it well.
PS: One minor correction, WebDAV itself does not support random writes. That’s a separate RFC that’s not part of WebDAV, but is perfectly compatible, and many WebDAV servers offer that functionality.