Couldn't you store more data in a color image? Just curious.

Probably, Microsoft did something like that (and failed to gain popularity) http://tag.microsoft.com/what-is-tag/home.aspx

I seem to recall it was used to print some HDCP keys on t-shirts.

There are likely many ways to increase the data capacity of a piece of paper.

The information capacity of the paper would depend highly on the printer, the environment the paper had to survive, and the camera.

Yes, around 3 times as much if the table on this Quora post is correct https://www.quora.com/Which-2D-barcode-format-has-the-highes...

Except most people's color printers are inkjet instead of laser, so the DPI penalty more than compensates for the 3x gain with color.

Colour ink has the tendency to fade with time.

Grasshopper (Rhino) is quite successful for architecture and 3D modeling, but its also tied to the engine. Also see https://news.ycombinator.com/item?id=7274674 for an exhaustive list.