I think you slightly misunderstood the TS’ problem.
It’s not that traffic wouldn’t flow as expected.
It’s that TF assigns paths in a rather strange way. After your crossover switches, you completely separated your lines. The TS didn’t want to do this. He wanted to have them run partly on the same track. In that case, you basically are dependent on your luck whether TF assigns tracks to lines the way you want to, or doesn’t.
Basically, the issue boils down to this:
Why does the game do it like that? That’s not only nonsense from a human point of view, but also is not even the fastest connection (because using the switches slows the train down). I could, in this rather simple example, solve the issue with a one-way signal, but the point is:
I shouldn’t need any signals forcing the line on their intended track, and it would be a bit of a hack. The TS can’t even do this in his setup, because signals don’t work for assigning lines to tracks.
This issue has very little to do with signaling, and very much with pathfinding for lines, which often is quite a PIA.