[Presence of ICC profile causes invalid chromaticities in saved PNG]

I think the main issue is accuracy. The chromaticities calculated by paint.NET from the ICC profile are a little off compared to the chromaticities used to define the profile in the first place:

         paint.NET  eciRGB
White x:  0.34576   0.34567 
White y:  0.35858   0.35850
Red x:	  0.67002   0.67
Red y:    0.33001   0.33
Green x:  0.20998   0.21
Green y:  0.71005   0.71
Blue x:   0.14000   0.14
Blue y:   0.08002   0.08

The sum of the Red x and y components is greater than 1, which they are not supposed to, hence the complaint from libpng.

[Presence of ICC profile causes invalid chromaticities in saved PNG]

If you open a PNG (rose_eciRGB.png) with an embedded ICC profile (eciRGB v2) and then save it as a PNG (rose_pdn.png), applications using libpng (like ImageMagick) complain about "invalid chromaticities" in the cHRM chunk.
The embedded ICC profile is gone as well.

This doesn't happen when saving as a JPEG. 

Edit: I'm using v4.3.6 but this has happened since at least v4.2.16

 

PS testImages> magick.exe identify .\rose_eciRGB.png
.\rose_eciRGB.png PNG 70x46 70x46+0+0 8-bit sRGB 10840B 0.000u 0:00.000

PS testImages> magick.exe identify .\rose_pdn.png
.\rose_pdn.png PNG 70x46 70x46+0+0 8-bit sRGB 9060B 0.016u 0:00.011
identify: cHRM: invalid chromaticities `.\rose_pdn.png' @ warning/png.c/MagickPNGWarningHandler/1746.