You're making a lot of baseless assumptions.
Quoting the ARMv8 Architecture Reference Manual:
A1.3.2 The Armv8 instruction sets
In Armv8 the possible instruction sets depend on the Execution state:
AArch64 AArch64 state supports only a single instruction set, called A64. This is
a fixed-length instruction set that uses 32-bit instruction encodings.
For information on the A64 instruction set, see Chapter C3 A64 Instruction Set Overview.
AArch32 AArch32 state supports the following instruction sets:
A32 This is a fixed-length instruction set that uses 32-bit
instruction encodings
T32 This is a variable-length instruction set that uses both
16-bit and 32-bit instruction encodings.
TL;DR: You have 3 instruction sets that have nothing to do with each other.
Furthermore, your claim that...
ARM32 machine instructions can be executed directly on ARM64 processors
...is not at all true for all ARMv8 CPUs.
If we look at the register description for ID_AA64PFR0_EL1
(page D13-3255
):
EL3, bits [15:12]
EL3 Exception level handling. Defined values are:
0b0000 EL3 is not implemented.
0b0001 EL3 can be executed in AArch64 state only.
0b0010 EL3 can be executed in either AArch64 or AArch32 state.
All other values are reserved.
EL2, bits [11:8]
EL2 Exception level handling. Defined values are:
0b0000 EL2 is not implemented.
0b0001 EL2 can be executed in AArch64 state only.
0b0010 EL2 can be executed in either AArch64 or AArch32 state.
All other values are reserved.
EL1, bits [7:4]
EL1 Exception level handling. Defined values are:
0b0001 EL1 can be executed in AArch64 state only.
0b0010 EL1 can be executed in either AArch64 or AArch32 state.
All other values are reserved.
EL0, bits [3:0]
EL0 Exception level handling. Defined values are:
0b0001 EL0 can be executed in AArch64 state only.
0b0010 EL0 can be executed in either AArch64 or AArch32 state.
All other values are reserved.
It is thus possible for an ARMv8 CPU to not support AArch32 at any exception level. And an example for such a CPU is Apple's A11, featured in the iPhone 8 and X.