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That log you quoted only shows chatbox tangentially, not as a core part of the problem. But there's no question HG's shared servers are being crammed full - all under the guise of 'unlimited' storage and bandwidth! And they aren't alone.

Nonetheless, as has been pointed out many times, any chatbox can be a real resource hog if you don't rein it in. Don't put it on every page, don't encourage people to sit in it all day long (forget sounds of any sort to notify them of new activity), do set your idle timeouts low.