I don't see a problem with the current storage system. I'd rather not make it easier for people to store out of frustration, as that might lead to more requests to unstore characters as well. "Quit store" is a really easy thing to type when you're frustrated in the heat of the moment. It's not too difficult to send in a storage request, and those particular requests typically get handled fairly quickly.
I think that just the act of having to type out an explanation as to why you want to store is a good way to keep people from storing out of momentary frustration that they may later regret, and this option doesn't really make it a whole lot quicker to store. I mean, you might be saving yourself what, 2 minutes? That 2 minutes isn't worth the potential downsides, in my opinion. Character storage of characters that are involved in plots creates holes in stories and is undesirable for the rest of the playerbase. We shouldn't be seeking to make it easier to do.
EDIT: Personally, I'd prefer that people seeking to stop playing a character get an ending to that character that drives story, rather than leaving a gaping hole in a plot where they just disappear forever. If a character gets stale or is not enjoyable, I'd support a request of some sort that gets said character involved in a plot that will likely end their life. That way, there is at least something left for other players to investigate or whatever. Something that creates content rather than destroying it. #RequestEnd
It would give staff a target for developing potentially lethal plots that wouldn't get people butthurt about their PC being killed by Staff plot, and might make that stale character a bit more exciting to play in the last bit of their life.