At the cost of drastically lowered productivity per person due to hot desking, and not having the space for an all hands.

Do you mean an 'all hands on deck' emergency or an all hands meeting? If the latter that's a problem with an event space not of desk space. If it's the former you rarely actually need everyone present and it's unlikely every department will be needed at once unless the whole company is failing and even then people can work remotely for those too.