I was just using my brand new drop-weight machine and admiring the design. Due to the design, there is very little tension variance between the bar being horizontal and a little off horizontal. As the OP pointed out, the tension is a function of the cosine of the angle off horizontal. But it's useful to note the small angle approximation for cosine is 1-((x/57.3)^2)/2. (where x is measured in degrees). Because the angle off horizontal is divided by 57 and then squared, for small angles the cosine is relatively invariant to the angle (because you're on the flat segment of the sine curve).
Approximate tension deviation (in percent) for error off horizontal (whether up or down):
1 degree: 0.015%
5 degrees: 0.38%
10 degrees: 1.52%
A 5 degree tilt is extremely noticeable because one end of a 2 foot bar would be about 2 inches higher or lower than the other at 5 degrees (and about 4 inches at 10 degrees). The drop weight is a simple and elegant design for achieving a precise tension.