The filesystem doesn't handle concurrency and atomicity of some operations well, while in web apps it is absolutely necessary - you serve multiple users concurrently and you will inevitably have some shared data.

I tried to avoid databases in my web projects in the past and ended up having quite complicated concurrency infrastructures, based on shared memory and the filesystem. I can't say I was happy with the complexity I got.

Databases, no matter how ugly, clumsy, handle it nicely. In a few cases I made a complete switch to DB and had my code reduced significantly.

So, for me this is still an open question.