>What's the point of this convoluted system? It allows voters to split their vote between parties. They can vote for a local candidate from one party and cast their second vote for a different party.

That's not really the point of the second vote. If we would only have the first vote we might have 599 representatives that only were able to get 20% of the votes in their district (the remaining 80% being spread across other candidates with a vote share of <20%). With the second vote we ensure that at least half of the seats are distributed proportionally across the parties and smaller parties have a chance to get into the Bundestag.