I think CFIT at high speed into terrain fits the horizontal spread of the crash parts and total destruction of the airframe rather than a vertical impact
I would be surprised if such an experienced pilot with a MC jet pilot alongside as F0 would take off with the pitot covers on ?
It is second nature to cross check the airspeed indications on the take off roll.
I had frozen pitot tubes where the pitot was switched off by accident and instincts are to push forward especially without outside reference.
But with pitot tube covers left on I cannot see two experienced pilots accelerating and rotating with no airspeeed indications!
If there was moisture in the pitot system and it froze soon after takeoff it's possible