There definitely is a cost benefit. We aren't in the 6502 era, videogames don't just call to the underlying ISA, they have to go through all sorts of OS services. There are services that PS4 games use that PS5 games don't, and supporting those costs money, more than just supporting the PS5 services (and spending the money introducing new services future PS5 games can take advantage of).
Ever fiddle with hardware that's come out after several hardware and software revisions and look at a table of which is the earliest firmware you can load on your particular SKU? That's because someone has to put in the work and effort of making the software compatible with the new hardware.
Indeed, we may even see something where "PS5 Next-gen UI 2.0" doesn't support PS4 BC and is installed on all the new revision consoles. "PS5 Next-gen UI 2.0 adds a bunch of great new features but removes support for PS4 backwards compatibility" etc. All they have to do is present it as a trade-off for "new features" and most consumers will gladly go along weighing the cost/benefit of upgrading. I already know what the defensive posts will say: "they aren't taking away anything from you, you can choose to upgrade to the new OS or keep the old one with BC support, you're so entitled". Then a year or so later when most people have upgraded they can quietly drop support for the old software entirely.
Everything costs money. Microsoft obsessively makes sure things are backwards compatible because that's their company culture, but other companies don't. There are plenty of old iOS apps you can't install on a new iPhone, despite those phone's chips still supporting the entire ISA of the earlier phones. And in addition to the expense of obsession with BC, it comes with its flaws: like Windows 10 having at least four contradictory design languages among its applications.