Perhaps if you live nowhere near an ocean and have no trees from which to hang a pendulum and can't afford a rangefinder for lining up two boards with holes in them.
I think you will also be surprised how hard it is to fill in the details of the experiments you are alluding to.
Also, ships do not always sink below the horizon. The right atmospheric conditions can refract the light in a way that causes them to be visible at a much greater distance than the straight geometry would allow. But this explanation can be inverted to claim that it is the vanishing that is due to atmospheric effects and that the non-vanishing ship is the accurate reflection of the geometry. Falsifying that hypothesis is, again, not so easy.
(Presumably this is also true at sunrise, so the day is longer than it "should" be from purely geometric considerations.)