For me, the GR keys belong down by the gold and blood shards, and have since you stopped having to move them into the slot to open a GR.
I agree that increasing the stack limit would serve the same purpose. However I disagree that they fall under the same category as gems (but wouldn't hate it if they were out of my stash as well ). I could even argue that they are a crafting mat. It is a stretch but they do "craft" a GR (hmm shaky). I still consider them a currency though. Oh and I have well over 1k keys.
The reason for this is that when I play multiple classes and switch between them, GR keys often get forgotten on another character. I know that the work around is to keep them in the stash, but it's an unnecessary extra step to have to stash GR keys after each regular rift, since being a tangible item no longer serves any real purpose.
Making them an account wide currency just makes good design sense at this point.