I was suggesting that you could use the barycenter of a binary star system as a point to build a LP.
Wouldn't Legrange points of stars be useless due to it leading to the middle of nowhere?
For the galactic orbits? Well, yes, because then you'd have a point about 1/6th of the galaxy away. But for companion stars they should create an exploitable Lagrange Point. IIRC though that doesn't actually shorten the distance to travel to the star.
That depends on the size of the two binary stars compared to each other. Stars that are similar to each other would have the barycenter and L1 almost on top of each other, while two very differently sized stars might have 90% of the jouney shortened.
Ex 1: 61 Cygni are close to the same size, so their barycenter and L1 are only ~3 AU apart from each other. You would still have to make 96.2% of the jouney the hard way.
Ex 2: Sirius A is almost twice as big as B, so their barycenter and L1 are ~5 AU apart (but the system itself is much smaller). You would only need to travel 75.9% of the way.
So even if there are 0 planets and LP in the entire system, you could still shorten the trip. And in both of these examples, if there is already an existing LP around a gas giant in one of the systems, then you would save even more distance. Travelling from an LP around a gas giant to the half way point between two stars still saves you half a trip.