A lot of people have forgotten but this concept was baked into the PlayStation brand for the first three generations. The PS1, PS2, and PS3 were all initially designed to be totally backwards compatible. A part of Ken Kutaragi's philosophy for the PlayStation brand as mentioned in interviews was that customers were building a lifelong library of titles with PlayStation that was respected and appreciated as a medium in the same way as collecting and trading music, films and literature are. The entire premise was that ANY current PlayStation could play ANY past PlayStation console's game at launch and enable thousands of games to be at your fingertips across each generation that could continue forward with you as an investment with long term value. This meant the consoles and games were less like toys locked to a single place and time, and more like living testaments to the art form just like decades of movies, songs and books that people own. It gave people the means to appreciate the breadth of the medium while seeing it's evolution unfold in front of them. While at the same time empowering them to share that media across decades without barriers to its enjoyment. There were even baked-in provisions for licensed publishers to have older PlayStation titles reprinted and redistributed as needed for new generations to enjoy, collect and trade, long past the point the systems those games had originally been on were discontinued.
It is "a matter of security… [PS2] offers a sense of insurance because it is compatible with PSone" – Ken Kutaragi, 2003 Speaking to Asahi Shimbun
This change to an aggressive anti-consumer stance that saw Sony eroding ownership didn't really start until the late PS3 era when Kutaragi was ousted from the company. While all PS3 consoles fat, slim, or super-slim can play PS1 games, general PS2 backwards compatibility was shifted from real hardware to a hybrid software approach, then abandoned entirely a few console revisions in to try and cut costs. Sony later paywalled a highly compatible PS2 emulator they finally developed for PS3 exclusively behind a small number of downloadable PS2 titles available on the PS3's PlayStation Store with no disc based support.
By the PS4 no backwards compatibility was offered at all while the brand and hardware was restructured in the wake of the PS3's complicated architecture. The CD laser included within all hardware revisions of PS4 hardware was even pointlessly disabled by Sony while their emulator for physical PS1 and PS2 discs was cut out of the console entirely and relegated only to downloadable PS1 and PS2 re-releases. But when the PS5 was being developed engineers designed and tested fully backwards compatible PS5 protoypes that were denied the green light for production due to then head of Sony Jim Ryan's famously public hatred of older games since he viewed them as ugly and worthless.
“When we’ve dabbled with backwards compatibility, I can say it is one of those features that is much requested, but not actually used much. That, and I was at a Gran Turismo event recently where they had PS1, PS2, PS3 and PS4 games, and the PS1 and the PS2 games, they looked ancient, like why would anybody play this?” – Jim Ryan, 2017 Speaking to Time Magazine.
Amazingly the classic PlayStation title reprint initiative Kutaragi envisioned back in the 90's is still alive and kicking. Even Sony themselves assured that physical reprints of older titles will continue on past 2028. But reports indicate Sony made it stricter for publishers in the late 2000's and early 2010's by locking some of them to the exact art and packaging as originally released (or re-released if the game was a Greatest Hits title), although some exceptions were made like with Konami's DVD-case style release of MGS1 for PS1 in the Metal Gear Solid collection on PS2. Some publishers like SquareEnix really believed in the concept of long term value from an inter-generational game library. They continued reprinting older PS1 and PS2 titles in their original formats until the late 2010's that you could still purchase new from their website until around 2024. Complete with registration cards and advertisements for merchandise, magazines, and surveys that all pointed to long defunct storefronts or addresses due to Sony's packaging and art restrictions. Official reprints of many PS2 and PS3 titles are still frequent from savvy retailer and enthusiast networks like VideoGamesPlus and GameQuestDirect, and even GameStop currently still has some new reprints of PS2 titles, such as VideoGamesPlus's most recent reprints of Monster Hunter for PS2 among other notable titles that showed up across many of their stores marked as "USED" despite being brand new copies of games (detectable as being in mint condition and using a newer style of PS2 DVD case when opened) when the GameStop Retro initiative expanded company-wide.
"Whenever, wherever, forever." – Sony, 2000 PlayStation's mission statement starting when backwards compatibility was introduced.
We still have CD's and Vinyl records as options for music, and formats people wouldn't expect like cassettes and Edison cylinders get new releases. But even in the digital realm giants like Apple have committed to DRM free downloads and giving buyers the ability to maintain real ownership of their digital purchases. So why are games the one medium in the history of humanity where digital-only is being pushed so strongly as to be forcefully mandated but done so with no ultimate right of individual ownership or future viability? People having the option to collect, trade, lend and bring their physical collections forward with them was for a very long time a fundamental part of PlayStation. It's sad seeing how mismanaged and completely uncaring of that Sony have been in the past decade and in particular these last few weeks. Physical purchases, even if a smaller part than digital, encourage brand loyalty, create life long customers, and drive positive engagement with both the brand and the medium by allowing it to become culturally significant across decades and centuries. It's only a matter of time before PS4 or PS5 backwards compatibility for digital titles is broken by a simple architecture change or shift to some new design philosophy in a future console. One where some future executive at Sony again asks "Why would anybody play this?” and all those digital titles people have spent thousands on become locked to some older console or lost to time never to be downloaded again. It shouldn't be this way, and if PlayStation's origins are anything to go by, it was never intended to be like this in the first place.
"PS one runs on PlayStation 2 through emulation [referring to certain facets of PS1 backwards compatibility on PS2] rather than actual [1:1] hardware. PlayStation 3 will offer the same compatibility for PS2 software and the format will continue forever." — Ken Kutaragi, 2003 Speaking to Asahi Shimbun
EDIT: To clarify the timeline of Ken Kutaragi's place at Sony and how it relates to backwards compatibility since several people have commented about it. Kutaragi announced his departure from Sony in April of 2007. Stepping down from his role included remaining as an advisor for Sony and the PlayStation division for about 18 Months. Sony launched one of their first non-backwards compatible PS3 console SKU's in late 2007 as a cheaper option, while existing backward compatible models remained on the market at a premium. In June of 2008 Sony discontinued all other backwards compatible models and launched their final backwards compatible PS3 SKU in the form of the Metal Gear Solid IV PS3 bundle. This remained on the market through summer and Christmas of 2008, and into early 2009 when shipments ceased and stock was depleted. By that point in early 2009 Kutaragi would have left his advisory role at Sony, and after this time it is known that no new SKU's of PS3 would contain PS2 disc backwards compatibility by default. But all PS3 consoles did at least retain full PS1 disc compatibility regardless of SKU or console revision.