The plots show if (how much) the variance (amount of dispesion on the Y-axis) depends on the expected value (position on the X-axis). Often, there is such a dependency when the "errors" are correlated with the response (typically for most concentration measurements etc). In such cases the points in such scatterplots look like funneling out (low variance on the left, larger on the right side).

Ideally, the amount of dispersion should be similar at all X-positions (predicted values = estimates of the expectation), and this is just as your plots look like. So that's perfectly fine. There is no need that the X-positions would need to be evenly distributed (or normal distributed, or whatever distributed).

If it happens that close to some X-positions (say around x1) there are many more points than close to another position (x2, say), it is expected to "see" some larger dispersion at x1 compared to x2, just because there is a larger chance that some of many values will actually be farther away from the mean than than for some of only a few values.

It somewhat is. But the real issue is the downward trend. This indicates that the likelihood term of your model is not correct. I recommend that you plot raw outcome against predictos. Adding a fitted line as well as a LOESS helps to uncover imprefections of the model. My best guesses would be that:

I don't see a global trend (as you mentioned "loess", I think you really mean a global pattern - what I don't see). The local pattern of series of decreasing values may due to an algorithm trying to reduce overplotting? If not, it can in fact be a model artefact, but I woudn't this consider relevant (because it's very local).

I suspect that the plots are due to some form of discrete response- counts or ratios of counts that need to be modelled properly.

Could you tell us the nature of the response.

also have a look at this

Parallel Lines in Residual Plots

Shayle R. Searle 1988

Article Parallel Lines in Residual Plots