Many/most Arduino boards are open source. So if you small and are trying to get a simple product line established you can start with designing a daughter/motherboard that the Arduino board plugs into for first series. Then, once you scale up, embed the Arduino parts into the same board. You can use a clone also, which can be much cheaper.

But I wouldn't go recommend Atmega328 for new designs unless its extremely simple, so when I say "Arduino" I mean something similar, like a Teensy 3+ or Olimex STM32 or Adafruit Feather M0

That depends on what the product may cost and how many you intend to sell. In general you might be right. But if you look in getting started and having a solution (suboptimal but working) quickly, then they are a good choice. Maybe not the best choice, but good.

The RPi (its SoC, really) is probably a fine choice financially for the applications where it doesn't represent ridiculous overengineering.