Crazy amount of texture bleeding

I've read many threads where people are experiencing texture bleeding, but none of the solutions seem to work. I've made a procedurally generated voxel world, where only faces visible to the player are created. I want to apply textures to the sides of the voxels. My textures are 16x16 pixels, and I've tried different sizes for the atlas, right now I am using 10x10 textures. I made one test texture of blue, white and black lines, and colored the rest of the atlas pink, but when I apply the texture (with correct UVs) I get a crazy amount of bleeding.

Coloring the surrounding pixels or padding the UV's does help, but I need a ridiculous amount of padding to make any difference. In this image the padding is so large I can literally only see the center 4 pixels of the texture, and there are still noticeable pink lines, so you can imagine how it looks with only 1 pixel of padding, everything is pink.

I've tried different default shaders, changing the "Non-power of 2" setting, turning off mip maps, changing wrap mode to clamp, changing filter mode to point, changing compression, disabling antialiasing, building the game and running it, nothing helps.

How do people solve this? I still don't understand why I can't just map the pixels onto every face. Is there alternative ways of texturing a mesh that solves this problem? Any help is appreciated.