This explanation is going to confuse non-photographers because for modern 35mm format lenses the difference between the maximum f-stop (which is purely the ratio between the focal length and the diameter of the aperture) and the maximum t-stop (the actual amount of light transmitted through a lens) are minimal (no where near full t-stops of light loss). Two lenses with the same focal length at the same f-stop with the same distance to the subject are going to produce the same DoF[1] and same exposure.
[1] To really understand how to calculate DoF for the format you are shooting with and the size you are viewing at, you also need to understand Circles of Confusion (CoC). The same (effective) focal length lens at the same aperture/focal distance and printed at the same size is going to give dramatically different DoF if one camera is 35mm format and the other is large format (8x10).
One thing we should also remember that because of the finite size of either silver halide particles in films or pixels in image sensors, it would not make sense to use very high F values - it would just not serve the purpose since once CoC is comparable with the size of the minimal light-sensitive particle/element, further increase in F will just reduce the amount of light without any increase in sharpness (e.g., a line which has the same width as the light-sensitive element would be recorded in the same way as a line which is only half as wide). For cameras with lenses that have very short focal length (such as, e.g., mobile phone cameras) pretty much everything is in focus (beyond a few dozen cm) even at low F (if you can control it, that is) - just because CoC diameter is so small it is comparable with pixel's dimensions of the image sensor. They are, in effect, "permanent focus" cameras.
[1] To really understand how to calculate DoF for the format you are shooting with and the size you are viewing at, you also need to understand Circles of Confusion (CoC). The same (effective) focal length lens at the same aperture/focal distance and printed at the same size is going to give dramatically different DoF if one camera is 35mm format and the other is large format (8x10).