In any random sample from a uniform distribution, there will be gaps and clusters. If you change the random number seed, the gaps and clusters will move to other locations. If you run my first example several times with different seeds, you will see that there is no systematic bias in the distribution of the points.

As to your comment about the marginal histogram, yes, the marginal histogram should be U-shaped. Uniformity on the ellipse does not imply uniformity when the points are projected onto the X or Y axis. In fact, you can prove that if (x,y) is uniformly distributed on the unit circle, that the marginal distribution has the density f(x) = 1/ (pi*sqrt(1-x^2)), which is a U-shaped density on the interval (-1,1).