>> ... but don't really know how putting some wear on the brakes will make them grab better.
There are volumes to read if you are really interested... but two things to highlight:
Despite our best manufacturing tolerances, brake pads and drums/discs are never "perfectly" matched in shape and flatness. Therefore, when put in contact with each other, there will be ridges, bumps, high spots, or just slightly mismatched shaping which prevent complete and even contact between the two surfaces. Under the initial usage, these high spots and ridges will see a disproportionate amount of pressure & friction, resulting in them wearing down faster than the rest of the surface. Over time (a comparatively short time), this is a self-solving problem, as the materials wear to conform to each other for a better fit.
So upon initial use, the brake is less effective... but after a short period of usage, the characteristics will have improved and stabilized considerably as the surfaces conform and make better contact.
A second factor is the initial conditioning of the drum/disc. Upon initial use, there is a transfer of material from the brake pads to the drum/disc, which alters the friction properties of the drum/disc. If you've ever changed the brakes on a vehicle, you might be familiar with the process of "bedding in" your brakes. A search for "adherent friction" will give all kinds of information on this subject, and how the initial cycling of a brake changes the properties of the surfaces.
(Note: I'm not sure that either of these are explanations of why the Speed Queens are indexing, just posting them as examples of why braking systems could be less effective when new, but improve with usage.)