I'm going to say "Yes, it's a good idea". Some of the time. And "It depends".
A lot of projects with microcontrollers involve external components, and there's a period of experimentation involved in getting those components to work in the way that they need to. That's when the characteristics of the Arduino might make it very useful--the ability to set up a working system extremely quickly, and operate it interactively using the pre-designed monitor connection, and make rapid changes in the functionality. Once all that has been done to the designer's satisfaction, it would be time to shift over to a smaller and cheaper processor. Perhaps that processor would be the same as the one in the Arduino, and perhaps not.
The reason not to use an Arduino for the initial work would be if there has to be a lot of processing involved, with libraries being used that won't work in a different processor. When it's more of a programming project than a hardware one, you probably wouldn't want to do the work in two environments because you'd end up having to do it from scratch each time. But the Arduino makes it possible to get hardware running very quickly, and that can be a useful way to start a project.
A lot of projects with microcontrollers involve external components, and there's a period of experimentation involved in getting those components to work in the way that they need to. That's when the characteristics of the Arduino might make it very useful--the ability to set up a working system extremely quickly, and operate it interactively using the pre-designed monitor connection, and make rapid changes in the functionality. Once all that has been done to the designer's satisfaction, it would be time to shift over to a smaller and cheaper processor. Perhaps that processor would be the same as the one in the Arduino, and perhaps not.
The reason not to use an Arduino for the initial work would be if there has to be a lot of processing involved, with libraries being used that won't work in a different processor. When it's more of a programming project than a hardware one, you probably wouldn't want to do the work in two environments because you'd end up having to do it from scratch each time. But the Arduino makes it possible to get hardware running very quickly, and that can be a useful way to start a project.