Physical address space is more than just RAM. It contains ROMs and memory-mapped devices such as APIC and video memory. The main reason you cannot use the BIOS outside of real mode is because it was recorded for use in real mode. Some functions may work in 16-bit protected mode, and will work more in Virtual 8086 mode, but trying to call the wrong function may cause your system to crash. In addition, interrupts work differently in protected mode than in real mode, so you have to reassign functions.
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