Bernoullis
You are missing one important point.. The principle stating the total pressure is constant applies to a given flow. Increasing the aircrafts speed gives you a new situation, a new flow. The total pressure is increased. For the Cessna taking off on the runway the static pressure is constant and the dynamic increases with the square of the speed i.e. total pressure increases.
And you may apply the principle even if you do not have any walls around the flow as in a venturi. The principle works perfect when calculating flows around a surface in an open flow of fluid.
You may derive the Bernoullis principle from the Work Energy theorem in physics. As Bernoulli most likely did.
best regards
Daniel Bernoulli is by the way son of the well known mathematician Johannes Bernoulli