you said : I don't see a single reason why would I design that in
but there are some reasons. for example very good and widespread libraries in Arduino IDE that makes every thing easy and fast.
Be aware that many of those libraries don't support the ARM Arduinos. The moment the library bypasses the Arduino wrappers and uses registers directly (e.g. to have faster access to GPIO or to implement a driver for some peripheral) it is not compatible and needs to be ported. Many of those libraries don't seamlessly support even the more obscure AVR boards - such as the Mega (has more peripherals and they are on different pins vs. Uno). If the board has anything else than ATMega168/328 on it, don't assume the library will work, especially when it is a 3rd-party one. It may or it may not.
also i should mention that the main goal of design an arduino on a pcb is having it's boot loader on pcb and be able to program it by arduino IDE.
For that you don't need to design in the entire Arduino module, just flash the bootloader into an ATMega and choose a configuration compatible with a common board (mainly the clock speed matters). Heck, you can even implement your "Arduino" on a solderless breadboard like this (google e.g. Boarduino).
ARMs all come with a standard bootloader in ROM, either a serial or USB one. I believe the ARM Arduinos use that too. Again, no need to design the entire Arduino module in just for this capability.
OTOH, if it is for a student project and the goal is not to re-implement the actual Arduino board (it is not very clear from your description of what your assignment actually is about!), just use it and focus on the core part of your project instead.