For example, say I ran a command to show disk space usage. Perhaps I would like to pipe the output into a d3 visualisation and see it directly within the terminal without context switching. Why shouldn't I be allowed to do this?

Have you read "The Visual Display of Quantitative Information" by Edward Tufte? Text isn't the best representation of all types of data.

Imagine also that I wanted to represent a table of data within an Excel style spreadsheet. This could be useful as it could define affordances for a user such as the ability to select rows and columns, and to sort or filter in realtime.

I can see the value in that, I don't see how looking across to a browser which has rendered the results of a command piped into a script is the end of the world.

One issue I have with bluring the lines is you open yourself up to a huge attack vector. If I can craft the output of my shell command to get code execution within your terminal I can now do anything, anything on any system you have access to.

Yes - it is a possible attack vector but that doesn't necessarily mean it shouldn't be attempted.