I assume you want to represent all of the relationships on the tree in any case, so I think minimising the number of required parent-child lines would actually make representing modern relationships less messy.

You'd have a pink relationship line for each partnership (that will be the same and just as messy in both approaches)

Then you'd have one child line from each relationship line to each of the children that came from that relationship, rather than two for each child.

So in a situation where Angus had 2 children with each of Beatrix and Chloe, you would have two child lines from the Angus-Beatrix relationship line and two from the Angus-Chloe line, rather than a total of 8 lines to show all the parent-child relationships in your current approach.

If Chloe also had two children with David then your approach would add a relationship line and another four child lines whereas the standard approach would just add the relationship and two more child lines.