The problem with always having one of these fun game modes to play is that they will have to have more work done balancing them. The other problem is that people will lose the attraction quickly and become "another ARAM"
This could be solved by.... Customizing your own games! ARAM would be easy to set up on Summoners Rift if you could simply have the option to disable top and bot Lane minions. Maybe teams could be changed from 1 to 6 players for 1v1s or hexakill on any map. Character selection could be set to blind, draft or free pick or something. You could disable characters, items, or whatever you wanted when you set it up.
Unfortunately, Riot has stated that it won't feature this kind of customization. This is a bad decision. All of Riot's competitors have options similar to this. Gamers, especially PC gamers, looooove to customize options and settings (hint, more key mapping options). As my game design teacher says (when talking about our one-week mini flash games): "That's a boolean! Barely a line of code!" And it can broaden the range of your player base massively.