System Arms with Doors Open

Almost every system works this way.  If you arm from the keypad the base will warn you that a door is open.  The purpose of this is if you want to leave say your bedroom window open and arm the system before bed, the rest of your house is still protected.

It is designed this way, as Jordan613 explains.   Yes, I would want it to arm with a door or window open.  I monitor my house and even with 2 kids running in and out, I monitor my doors and windows.  If something is open then I'll likely know about it.  Arming the system and being notified that there's a door open (from the base) is another way I can keep up with everything.  If you're arming from the app then I assume you aren't home, and if you have doors or windows open then you may have other issues to address.  If I left a window open and went to work, then needed to arm the system remotely with the app, then YES, I would most certainly want my alarm to arm.  I would much rather have it armed that way than not at all.  I'm not sure who you talked to at Simplisafe that agree with you, but this is how the system has operated for years.

I would rather it arm with a window open than try to arm and have it fail.