(This is one of a series of Software Engineering Maxims Which May or May Not Be True, developed over the last few years of working at Google. Your mileage may vary. Use only as directed. Past performance is not a predictor of future results. Etc.)
There are going to be emergencies. It happens, despite our best efforts to anticipate risks. When it happens, we go into damage control mode to resolve it.
People not involved in handling the emergency will begin to ask about a postmortem almost immediately, even before the problem is resolved. It is important to not begin writing the postmortem until the problem has been mitigated. Doing so turns a unified crisis response into a hotbed of fingerpointing and intrigue. Even in a culture of blameless postmortems, it is difficult to avoid the harmful effects of the hints of blame while writing that blameless postmortem.
It is fine, even crucial, to save information for later drafting of the postmortem. IRC logs, lists of bugs/CLs/etc, will all be needed eventually. Just don’t start a draft of a postmortem while still antemortem.