Are you certain using AES is still faster? Let's say for a 32-bit block size and 64-bit key.
From https://en.wikipedia.org/wiki/Speck_(cipher), that Speck combination would use 22 rounds, and using the instruction timings for Zen 5 from https://instlatx64.github.io/InstLatx64/AuthenticAMD/Authent..., it looks like each round would take at most 3 cycles. (Dependency chain for each round is 3 instructions long, ror+add+xor). 22*3 = ~66 cycles.
Using AES with a pshufb to take out the ShiftRows step would be 2 cycles for the pshufb and 4 cycles for each aesenc, and at 10 rounds, you have ~60 cycles.
It's quite close, and to say which one wins, we'd need to actually benchmark it. One is not clearly much faster than the other.
maybe the reason they are so close is that the AES microcode is inplementing exactly those operations
There's nothing similar about AES and Speck, and the "microcode" for AES isn't like what you're thinking of. If you want to learn more about it, you can look up the specifications for AES and Intel's AES instruction set.