Sony and Microsoft used to pay for exclusives without buying the studios. So there's no real meat to the argument that "oh, the games were always exclusive because first party" or whatever. The consoles didn't really buy that many game studios until relatively recently in gaming history. They would pay a studio to not release on other platforms. This whole buying studios thing was just cheaper in the long run. So there's no real argument to be made about Sony just making better first party games. That's what they do now given that they own the studios. Both companies are guilty of buying out studios.
Exclusives pre-dating the PS1 was more out of lack of technology. No cross platform tech really existed. There wasn't a lot of crossover. Many platforms didn't last more than a generation or two. There wasn't even much cross over in the kind of games. If you liked fighting games, you bought a Sega over Nintendo for example. With the PlayStation, they competed against Sega first, Nintendo as more an afterthought. Xbox came in later to compete against PlayStation 2. The Nintendo 64 was just a different class, and even later, the GameCube. With Xbox and PlayStation, they had similar amounts of power and restraints (an N64 cartridge could not compete from a technical perspective against the storage of discs, plus multi-disc games could exist, not really feasible with cartridges) plus abstraction technology was more advanced and one could more easily write cross platform code. Now, you either had to pay for an exclusive or simply hope they only had the intent to target one platform (whether through preference or resource limitations). So the console wars really started to heat up after the death of Dreamcast and mainly between Sony and MS. Exclusivity wasn't via first party existed, but not to s great extent beyond their flagship games.
So, tldr, exclusivity has always been acquired via money and buying them. It's easy to say it's about developing better first party once those studios were bought outright to begin with. That's how most first party titles exist now.