I'd recommend something cheaper and simpler like the STM32F4 discovery boards. You won't get linux and will have to program via JTAG but the documentation for the STM32F4 is not as overwhelming as Broadcom's.
For a related twist the OP might check out the Nordic Semi's M4 with radio SoC offering, the nRF52840DK. It has an onboard, breakout-able segger JTAG programmer and is easy to get going with Segger's freebie take on a GCC IDE.
In reality every vendor's peripherals, and more importantly HAL and associated drivers and libs, will be different. But if you've done it once learning another vendor's way of life is a bit like learning a new programming language; it's just syntax.
Broadly most (IE communication, ADC, watchdog, etc) peripherals will be similar but there are definitely places where the differences will be larger. I'd expect those to be largely focused on clock trees, interrupt architectures, power modes, etc.
So short answer I agree with parent, get a cheap board and learn some stuff. If you like it, go from there. Do NOT choose a Cortex A though unless you want to really dig into embedded Linux. Systems at that level are way, way more complex and if the goal is to learn "everything about this processor" that will be especially difficult.
General ARM programming--yes.
Specific peripherals--no.
General peripheral knowledge--yes.
An ARM is an ARM withing certain limits so your knowledge transfers. Sadly, every chip has a different way of programming the periperhals. However, every chip has roughly the same core peripherals (I2C, SPI, UART, etc.), and those electrical specifications and how you use them for protocols doesn't change.
General peripheral knowledge--yes.
Except for the Kinetis DMA, I never understood that one!!