PS3 had great emulation of PS1 games, not sure why Sony didn't just bring their emulator over to PS4 and PS5. Also handy that every PS3 could read PS1 game discs. Every PS2 had the PS1 hardware all contained on a single chip, if I recall correctly. PS2 could also read PS1 memory cards, and use PS1 controllers. I remember when PS3 had hardware-based PS2 back-compat, but they eventually took that **** out in newer revisions, I think due to manufacturing cost reasons? I wouldn't expect PS3 emulation on PS4 considering how PS3 emulation on PC still isn't 100% there (but very good progress has been made, and some games are fully playable, at higher resolutions too). I figured PS4 being AMD64-based would mean it shouldn't be too much trouble to get those games working on PS5. I think PS5 should be powerful enough for PS2 and PS3 emulation. Sony probably doesn't wanna spend the resources to develop full blown emulators. They'll probably throw a few individual games from older systems up on the PS Store for us to buy, like some of the PS2 games they have on PS4 (and I think PS1 as well).
Back-compat is always appreciated but I don't automatically expect it. As someone who holds on to all their previous systems, back-compat has mattered less for me. Then again, sometimes it works out for specific reasons. Like how my PS2 Slim no longer reads discs, so I'm currently out a PS2. I did appreciate the faster loading of PS1 games it offered. My PS3 doesn't have PS2 back-compat, and emulators on PC (at least PCSX2) can't run every single game I have. I have a working PS1 but I usually use an emulator on PC, or my PS3, for PS1 games.
XB1 works out really great for original Xbox games, and Xbox 360 games. Original Xbox games look ****ing fantastic on XB1. I still have my X360 hooked up cuz not all my X360 games work on XB1. I also have one original Xbox game that doesn't work on X360 or XB1 (MK Shaolin Monks). Unfortunately my sister and her husband borrowed my original Xbox years ago, and have since lost it somewhere in their house, so XB1 is where I mainly play my original Xbox games. My XB1 is mainly a system for X360 and original Xbox games. Cuz any XB1 game I'd want to play on XB1 I play on PC.
Wii is handy for running GCN games with Component video, cuz Component video cables for GCN are expensive as all ****. Back in the day you could only get them direct from Nintendo, and I scoffed at their $30 price when I was used to paying $15 for S-Video and Component cables. Well now on eBay those GCN Component cables routinely appear for prices like $200, so yyyeeeaaahhh... Anyways Wii is kinda an annoying system to deal with, so I prefer to run my GCN games on the actual GCN. Still, I appreciate the hardware-based back-compat.
I appreciated Game Boy Advance being able to run GB and GBC games. DS could run GBA cartridges. 3DS could run DS cartridges. So that kind of stuff was always nifty.
I remember when Saturn came out, I was disappointed it wouldn't run Sega CD games. I didn't expect Dreamcast to run Saturn or Sega CD games though. I keep forgetting that Mega Drive/Genesis could play Sega Master System games with the right adapter.
Anyways while there are many examples of console back-compat, it's never a given. I don't look to each new generation expecting those new systems to play games from any of the previous generations. Nice when it happens, but not having that functionality is not the end of the world. PC is still the best back-compat system.