After reading this, I found that there isn't much of a difference between error, notice, and alert and that you can put whatever you want in the flash.
However, I noticed that there seem to be built-in methods for getting the notices and alerts from the flash in views, but no built-in method for retrieving error messages.
I was wondering why this is the case. Is the use of error in the flash discouraged?
No, using flash for errors is certainly not discouraged and in fact part of the official documentation.
You are seeing accessors and built-in methods for alert and notices simply because they are the most common ones. As you might have seen in the linked questions, flash is just a hash and you can use any key that fits your application well. I believe common practice, at least from my experience, is that :notice is for messages that report a correctly completed task, :alert for non-showstopper errors, and :error for showstopper errors.