To be fair that's because software on consoles is designed for specific hardware. With newer hardware the old games won't just work, because they were complex for very specific hardware. So for BC you end up with emulation which requires a lot more processing power than the original hardware, and is not perfect.
Or using the old hardware like the PlayStation 3 BC for instance, they literally had the PS2 hardware in the PS3 to handle BC. And as time went on they removed that hardware to save costs and BC went with it.
PC gaming however, and by extension portables like the Steam Deck however are running software developed more generically for wider ranges of architecture to begin with. It means less hardware optimization, but it generally means compatibility out of the box as hardware improves since it wasn't designed with extremely specific hardware anyway.
This is less true since the PS4/XB1 era, since it's just pretty standard x86 hardware, much like a PC. Although it may still apply to the Switch if they go in a different direction for the Switch 2.
Not removed per say, they switched from using a Native IOP like the PS1's processor to replicating the functionality with a PPC chip, codenamed Deckard. The emulation isn't as good as original hardware, and PS2 games which used features of the IOP chip can have bugs as a result.