Don't know about the Tower Air incident, but Continental's DEN incident was unrelated to taxi speed. They were in "position and hold" (old time terminology!), and subsequently cleared for takeoff. Then they started rolling. After > 2000' of rolling, either a gust in left crosswind, or insufficient rudder (or a combination of both) caused the aircraft to start veering to the left. At this point the Captain elected to "assist" the FO (who was the PF) by using the tiller somewhat, instead of either aborting or calling for more rudder. That caused the nosewheel to turn to the right, and essentially "rubbed off" the tires, since the plane was still going on the same path.
This incident was NOT related to taxi speed. NOT related to hurry-up culture. (Unless of course, you're suggesting that Southwest's culture is somehow to blame for other carriers' accidents).
Try again, Dan. Or not.
Bubba