Single stash games are convenient for a variety of reasons. A would-be player only needs to buy one stash to start playing these games, and thus the low cost barrier can make them a lot more accessible than, say, Zendo or Gnostica. A single stash is that much more portable, so these games aren't just for home play. They are also that much quicker to set up and clean up, since there are only 15 pieces to deal with and you don't need to sort them by color, so they are great for playing in a restaurant or coffee shop.
Single stash games lack the ability to use color to distinguish the pieces, which means there are fewer axes of variation. Since color is frequently used in other games for telling who the pieces belong to, some other feature is needed to deal with that. Having pieces point towards or away from the person they belong to is a common solution, as well as having games that don't involve ownership of the pieces. Also, 15 isn't many game pieces, especially if there are more than two players, so several single stash games work as solitaire games as well.
See our list of single-stash games under Category:Single stash.