Even if the “grand coalition” staggers on, Mrs Merkel should not hang around for long.
The CDU, when it gathers in December at the congress that will now choose a new party leader, will be aware that it is also choosing the probable next chancellor, which is why three powerful candidates jumped into the frame on the day she made her announcement.
Others are likely to follow. The winner will instantly upstage the incumbent.
As well as being speedy, the process needs to be transparent.
On migration policy, euro-zone reforms and defence, the CDU has large disagreements that need to be hammered out.
The choice of a successor to Mrs Merkel is the time to do it.
There should thus be a genuine debate about principles and, above all, no attempt by Mrs Merkel to push forward the successor who would be the most likely to prop her up.
So far she has not entirely lived up to that ideal.
It is widely understood that she wants Annegret Kramp-Karrenbauer to take over (she nominated “AKK” to the post of party general secretary in February with just that in mind, many believe).
Ms Kramp-Karrenbauer, as far as one can tell, shares most of Mrs Merkel's centrist instincts.
The other two declared contenders, Jens Spahn and Friedrich Merz, are considerably further to the right.
Either of them might help the CDU stem the haemorrhage of votes to the Alternative for Germany (AfD), but would alienate the Social Democrats, assuming they remain in the coalition that long.
Once Mrs Merkel steps down as chancellor too, Germany ought quickly to hold another election.
Leaders without a mandate from voters seldom command much respect.
And the electoral situation has changed radically since the last vote, in September 2017.
The coalition parties' support has collapsed, thanks to the unpopularity of their reheated deal;
that of the Greens and the AfD has surged.
Germany's government needs to reflect that fact if it wants to get anything done.