In previous eras (1980s, 1990s, early 2000s), hardware differentiation and game exclusivity were part of the same equation. Why? Developing for a wide variety of hardware configurations was exceedingly difficult and a significant component of cost. If a studio developed a game for the Xbox 360 (for example), it took significant re-engineering (if not impossible) to run that same game on a Nintendo product, or even the PS3 (thanks Cell).
The further back in time you go, the more exclusivity made sense to the development team. They could focus on one build and a collective audience, while sometimes taking a payment from the console manufacturer for partnering with them (if they weren’t already owned by the console manufacturer). Keep in mind that it was often difficult to even get a version running on the target console, or PC, thus the focus on one build. If the money worked out, the development team could always try a “port” later (rebuild the game for another platform). Regardless, exclusivity was often a competitive deal for many developers. Hardware, for the most part, drove the underlying structure of how the industry operated.
Today, hardware is vastly more standardized and most of of the technology has coalesced around a handful of APIs. In fact, most modern engines already cross-develop across Nintendo products, Xbox / Windows, and PlayStation. Building cross-platform isn’t like it was in the 2000s (and prior). Cost, primarily, is driven by large development teams (AA and AAA products) and modern salary requirements (not technology restrictions). A game team can cross develop a game from the inception of the concept, but they often have to pay 100-500 people to do it. Hardware isn’t driving exclusivity, unless it’s Nintendo. (Nintendo can do so because of their history, catalog, and hyper focus on hardware as a core product. That’s an article for a different time.)
Exclusivity today, for Xbox and Sony at least, is almost entirely due to back room business dealings, purposeful “walled gardening” or first party restrictions (all business focused purposes). Ultra restrictive partnerships with a console manufacturer don’t make as much sense because it cuts millions of end consumers out of the revenue stream. Even first party studios are targeting PC releases, save for a handful of exceptions (because not doing so leaves money on the table).
“Money-hatting” (assisting with development expenses) can’t cover the growing cost of these large teams, thus you see most of the large publishers distancing themselves from being paid for development, bonuses, or creating games for one platform.