You've got to ask what caused that tire to fail, and what did that do to the rest of the truck? To the engines? To the structure? To tilt? Slow leak out there, insufficient to activate a hydraulic fuse? When the tire failed, what did it do to the other wheels on that axle, or truck? Increased load, increased temperature. Going to put the gear up and have one fail in the well? Pieces hanging off? is the tilt going to be a problem, and is indication and logic going to function if something just catastrophically failed down there?
Once more; we're talking about a known or suspected tire failure.
Various aircraft have interlocks that prevent raising the gear; "safety" catches, releases, solenoids, etc, which prevent raising the gear unless certain conditions are met. Most have checklists under abnormal or otherwise which allow bypassing the gear safety lock.
Doing so is not always the right choice. Nor is raising the gear with a known gear tire failure.