Outside of the New Years speech, German chancellors generally don't do "TV speeches" (I recently saw a number of only 5 other cases where they did: Iraq war, Kosovo war, 2x reunification of Germany, RAF terror). That of course doesn't mean things they say aren't distributed, just that it's unusual as the formal address to the nation. E.g. they can speak in parliament, and we might see that speech or snippets of it distributed. And they do give statements to press.

Not sure how much of a role the split plays, e.g. the President doesn't do it that much either.

For Merkel specifically, she's generally happy to let others do the talking, observe the reactions and then act according to that, in what one could call a fairly passive style.