Incorrect results will manifest. If you take the dot product of a surface normal and another vector and they aren't the same length, the dot product will be distorted by the lengths of the vectors.
Ray direction and ray length might be combined into one vector that just stretches from the origin for ray tracing, but using the direction with a surface normal for dot products, reflection vectors etc. is going to give artifacts.
What you say is true; however, not automatically normalizing ray directions after transformation can be useful in some cases, e.g. to avoid introducing floating point error when calculating points from t values.
I literally gave using the non normalized ray for ray tracing as an example.
(Also in practice floating point inaccuracy doesn't become a huge problem since you have to design around floats not being exact in the first place. Spheres can also wind up being more finnicky with precision but are rarely used as primitives to trace against in production renderers. There isn't a single right way to do the tracing, but the shading does need normalized vectors for a lot of common operations.)
It's because tracing a sphere is quadratic equation solve. The guy in the video, Eric Haines, published an article about how to improve sphere tracing precision. It's in the freely available Ray Tracing Gems book.
Spheres are the "hello world" shape of ray tracing, but are generally not used for production renderers for the following reasons: Spheres are not that interesting to render, because hardly anything in the real world is a perfect sphere; and determining a ray-sphere intersection point requires solving at least one quadratic equation, which requires a square root, which is slow
Triangle meshes are better choices for the same reasons: they can be used to model arbitrarily complex shapes, and it's faster to compute ray-triangle intersections.
Ray direction and ray length might be combined into one vector that just stretches from the origin for ray tracing, but using the direction with a surface normal for dot products, reflection vectors etc. is going to give artifacts.