Bare metal ARM cortex M programming sequence
It is not standard. The peripherals are different between manufacturers. However, within a manufacturer, the peripherals tend to be very similar (to encourage you to stick with their products since once you use one it is much faster to move between their products than someone else's). For example, I use the STM32F303 on Segger IDE and the steps and register names are identical (due to CMSIS) to yours.

Only the ARM core is the identical, which mostly doesn't matter to you as an high-level language programmer). 

Since writing libraries is a lot of work...choose the manufacturer you want to learn with carefully. You're probably going to be together for a while.

Regarding your I2C comment, sure the data transmission on the OUTSIDE of the microcontroller might be the same, but that in no way shape or form means that it has to be organized and configured the same way inside the microcontroller. That's like saying because two people can talk to each other, they must both think and act alike.