Imagemagick: replace alpha pixel with color-shade pixel

Question

In previous question I made false assumption that I need to remove pixels with alpha, but I actually need to use alpha percentage as shade of white.

Because just removing alpha-pixel changes lines. But as background is to be white.

Image btn_bg_common_press.9.png

becomes

I also looked at ImageMagick, replace semi-transparent white with opaque white and found that I can do with

convert icon.png -channel A -fx "(a>0.5) ? 1.0 : 0" output.png

Though that is still rough.