It is cheap only if you don't change CPU or GPU architectures. This is why the PS4 doesn't have PS3 compatibility.

When apple switched to ARM even with x64->ARMv8 translation layer (NOT emulating) it was still noticeably slow in a lot of software. Even though some x64 games worked on ARM macs they still lost A LOT of performance.

The backwards compatibility of the PS2 was due to the PS2 literally including an extra PS1 CPU (technically PS1-like CPU underclocked to match the original PS1 CPU when running PS1 games). On PS2 games this PS1 CPU handled only I/O so it wasn't completely wasted when running PS2 games.

https://en.wikipedia.org/wiki/PlayStation_2_technical_specif...

The PS2 CPU is a MIPS III while the PS1 CPU is a MIPS I. I am not an expert but I think but I think MIPS III is only backwards compatible to MIPS II, not MIPS I