My bike fell over more often when it had a kickstand.
Without one I lay the bike down or lean it against something sturdy, which seems to work better. A bandana will protect bits of the bike you don't want contacting walls, etc. A broccoli band wrapped around the front brake handle (keeping it engaged) will keep it from rolling and flopping.
Now, for a cargo bike (like a Big Dummy or Yuba Mundo or Kona Ute) I'd definitely get a two-legged heavy duty kickstand.
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson