As far as I can tell, there is no way to write to or read from custom files on the Cortex via ROBOTC. Why is this functionality not available for the Cortex when it has been there for the NXT for a while? Is there some technical reason that it cannot be implemented?

This is actually something that we began to implement in a much earlier version of ROBOTC. We began with support for storing multiple user programs on the Cortex, with plans to also do the file I/O.

The problem that kept us from going further down the path was usability/confusion vs. end-user demand. The NXT has an LCD screen built right into the device, with a small UI that allows users to navigate through multiple programs. With VEX, the LCD is separate and many users don't have them. In the version(s) that we included multiple file support, many users accidentally downloaded multiple programs, but didn't have the LCD, and became confused when their programs didn't just run. We stripped the existing functionality out since there wasn't much demand for the file system, but a fair amount of difficulty with usability.

That said, multiple file support and file I/O hasn't been taken off the table permanently. It's something we can and will revisit if users want it, and any input you have regarding what you'd like to see will definitely be appreciated and considered.