This notepad is designed to behave just as you expect it to. Notes are always automatically saved. They can be easily exported to any app, such as email or Dropbox. The notepad is also a share target from other apps. You can even tell Notepad to remind you about something you wrote, with only a couple taps.
On your home screen, it appears as "Notepad" instead of "Simple notepad".
Also, it's open-source! https://bitbucket.org/nkorth/android-notepad