Milko is correct that in Germany, you vote for the party - not the leader. In the UK, you're supposed to vote for who you want your local MP to be, but of course people often end up looking at May, Corbyn etc. and using that to make their decision.
However, the other way of looking at it is that more people voted for Merkel's party than anyone else, so she's the most deserving leader. After her, the next party was the SPD with only 20% of the vote share. Surely it'd be even more strange to have a leader that only 1 in 5 voted for?
As it is due to the coalition process, by the time the parties have come to an agreement, the ruling coalition will (between them) have over 50% of the vote, and hence have a mandate to be in power. It's just that politicians and parties have to work together to achieve it.
On the plus side of the German system, the only votes that are essentially wasted are for parties with less than 5% of the vote share. In Britain, only the winner of the constituency counts, which means lots of tactical voting and wasted votes. Vote for the Green party in the UK and it's usually a wasted vote. Vote for them in Germany and you're directly affecting the Bundestag as the Greens have 8.9% of the vote, and hence 9.4% of the seats.
EDITED: 29 Sep 2017 16:08 by DAVE!!