So, reading above it seems to say that the Blitz run is not designed to hold a weapon; however, when you activate a shield and/or sword, the Blitz run proceeds with the weapon until a certain time has passed or you jump and the animation is reset; at which point, the run goes back to the default. So the movement CAN hold a weapon, it just looks a bit dumb and it doesnt stick. I would honestly be fine with it looking dumb and my character repeatedly stabbing themself in the face if that meant not having the run change jarringly and almost randomly mid-sprint.
When it comes to utilizing the run with the a weapon-based character, I think it should either be 100% on or 100% off. It looks/feels whack to have it turn on and off randomly while in the midst of running with a sword/shield out.