I can agree on moiré. When you have a finely detailed texture with a repearing pattern that comes close to the resolution, you can get moiré effects. A workaround is indeed a slight blur. It's not a    soltution as you lose detail, but when done by someone with experience the slight disadvantage outweights the moiré pattern problem.
Bicubic uses 4x4 pixels: horizontal, vertical and diagonal. It's considered to be the best balance between calculating time and result. There are better algorythms, but these are often linked to expensive plugins or standalones.
But the problem remains the same: making the grid smaller means averaging hues. Of course it's better to have each pixel "watch round itself" to every pixel that surrounds it (bicubic) but if this happens in long series -to get rid of a lot of pixels in one step- more image is lost that when you do the same in several smaller steps. True, you may lose more in the rounding to integers, but you win more than you lose.
Look at the image: the left pattern was downsampled to half in one step, the right one in four steps. If you look closely you'll see how the four steps create a nicer set of pixels to come close to the original.
Hey, I didn't invent this! Just read what most Photoshop gurus write. It's from them I learned this trick. If you have to resize only a little, this doesn't matter. But if you resize a lot it's visually better.

You always lose detail (information, data) but less when you take the stairs instead of jumping through the window.

There are no Borg. All resistance is fertile.