It will be a must once mobile is launched, which I'm working on.

Is it also possible to use multiple devices without leaking from which device each message was posted?

Well, yes and no. The log will show a different id (public key) which authored the message. But the device itself (iPhone or Google Nexus or whatever) doesn't need to be mentioned.

That could leak information a user doesn't want to be leaked, like at which hours he is at work (using the work computer) etc. Which id belongs to which device could probably be inferred when the service is used actively.

I understand that transparency might not be a design goal or techinically possible, I'm just raising the concern.

Can't I just share my private key across multiple devices?

Nothing stops you from copy-pasting your asymmetric keys (it's a file) to different devices. I bet it's feasible, the biggest issue is also making sure your log stays the same, because a log shouldn't get forked.

Those sound like pretty unavoidable, and often acceptable, drawbacks.