Offline mode works the same for me as well. I can only go offline if I am already online. But if my internet goes out unexpectedly, it is impossible for me to play any Steam games (except for the rare exceptions where the drm is not incorporated into the .exe.) I have tried every trick in the book including pulling out cables, turning off ethernet adapters, turning off wireless adapters, checking and unchecking boxes, etc. I'm not sure how common it is, but it's certainly not unheard of. This topic has come up multiple times both in the predecessors to this thread and other threads focused exclusively offline mode and multiple people have confirmed it behaves the same way for them. If you contact Steam to ask them why, they say it's working as it is supposed to.
And in reality, this is how Valve themselves
say Steam offline mode is supposed to work.
So it's not that it's broken for people like us, it's just that it works better than it should for others. Yay?