About your remark about "pure physics": in engineering when working with SI units, the EuroCode basic wind pressure is 0.625*W^2 [Pa], where 0.625 is just half of "standard" air density. ASCE 7 considers the coefficient of 0.617 instead 0.625 because they have other "standard" conditions.

Considering the height of interest for structures under discussion here and the above equation, the only reason the wind pressure changes vs height is that the wind speed changes vs height.

In engineering, few decades ago a speed wind profile power law with exponent 1/7 was very popular. As a result, a power law with exponent 2/7=1/3.5 (or even 1/4 or " double square roots" rule, more friendly with an "ancient" hand- calculator) were applicable for wind pressure. ASCE Code and European Code just follow more sophisticated equations. But always a minimum pressure has been considered, otherwise near ground calculation will impose near-zero loads.

About your issue: by ASCE 7-10, 29.8 MINIMUM DESIGN WIND LOADING
The design wind force for other structures shall be not less than 16 lb/ft2 (0.77 kN/m2) multiplied by the area Af.
However, for ASCE the design pressure is- in their terminology- qz*G*Cf, so is not so simple to find out to which speed corresponds this minimum design pressure i.e. 16 lb/ft2 (0.77 kN/m2). As I know Caesar calculates "G" and consider it in calculation, however doesn't report it as value.