You can improve UV coverage a bit but removing redundant duplicate baselines. Which is what pseudo-random patterns do. And these are used e.g. by Lofar. But the problem of lacking very small baselines to fill in very large scales on the sky remains. Interferometer are simply not very good for imaging extended objects. And of course the other thing is that you might have less reflective area in total and thus lower sensitivity for dim things.

It isn't a random pattern, but yes.

A logarithmic expansion of baseline distances seems to be the first thing you want in a sparse array. Ideally you want to be able to look in all directions with about the same amount of sensitivity and angular resolution. But the UV coverage of even an asymmetrical, relatively sparse array like the VLBA is surprisingly good, because as the Earth rotates, the antennas describe sweeping arcs on the sky.

The regular UV coverage of the VLA is great, though, for sensitivity at short duration observations.

But Arecibo was great for pulsar work. :-(