Cutting down broken blades into smaller blades is a tradition as old as blade use. There is such tremendous variation in the katana itself that some were barely longer than some wakizashi. The short katana schools of fencing felt that closing in was best, while on the other end you have the long katana schools with blades a meter long. There is the same kind of variation in wakizashi as well, with some being more like a CS magnum tanto and others long enough to almost be a katana. Katana made specifically for better were thicker, heavier, with a more robust grind than an heirloom sword, and we have fewer examples of these blades since they were routinely bashed to Hell. A sturdy wakizashi would seem to be a great thing if one were to try and stab down an armored opponent, and on the other end I have seen a thin, light wakizashi where a full third of the blade was after the yokote. It looked like it could cut you by looking at it, and stab you by pointing.
So that's basically a non-answer that sums up to "it depends." One thing to remember is that the primary weapon of the samurai was the bow, followed by the spear. The Katana was a secondary weapon, and sometimes tertiary if the fighter in question favored axe or club. Unless it's a two swords school fighter, things have gone really badly if the wakizashi has to come out.
