Why did Canon and Nikon introduce new lens mounts for their mirrorless cameras?

The E-mount and Micro Four Thirds were already open mounts they could have taken advantage of, or gone the Pentax route and introduced a mirrorless based on their existing lens mount. The MFT mount has so many lenses because several manufacturers got together on it. Nikon and Canon could have joined up with Sony on the E-mount to do something similar, or got on the MFT band wagon.

What's more is that both of their mirrorless offerings are crippled and seem to make very little sense. It's like they were afraid to make them good and compete with their own DSLRs.

You can't use DSLR lenses on an EVIL, except the Pentax K-01, because the back focus is too short to allow infinity focus. Look how bulky the K-01 is compared to similar cameras BECAUSE it has to accommodate a DSLR's back focus.

Sony developed the E-mount because they wanted people to buy their lenses, despite the prior existence of the 4/3 mount, and Pentax use a different mount on the Q. Sony also make an adapter to use your DSLR lenses at a price bordering on extortion.

Canon and Nikon produced their own mounts to ensure customer loyalty, just as Sony did.