console wars are why we have good games in the first place, forgetting the war is how we end up with no games at all. All those companies lost their way and are no longer competing with each other. Now they just match each other's constantly rising prices. Back during the old console wars, they would compete with the lowest prices and the customer would win every time.
I think the console wars ended at the start of either the eighth or possibly the seventh generation.
TL:DR: Console hardware unified with the rest of the tech industry, defeating the point of exclusives altogether. Read on if you want my long-ass explanation.
From the eighth generation onward (ninth for Nintendo), the hardware was standardized to common devices (X86 for Xbox/PlayStation and ARM for Nintendo). The generation before, all three systems used (vastly different) PowerPC architectures.
(I'm kinda putting Nintendo into both Wii and Wii U since they didn't align exactly with the timeline due using PowerPC in the eighth generation).
In the prior (sixth) generation, it was still kinda weird. Nintendo went with PowerPC like the Wii/Wii U, but it was the first time out for a console to do that (barring the Pippin but I don't even think Apple counts that anymore). The PS2 was the weirdest one by continuing on from the PS1 with a RISC-based MIPS processor. And while the Xbox was effectively a PC, it was a really weird proprietary one with a black box of an Nvidia GPU. Even the Dreamcast (much like the Saturn) used a custom CPU from the company mostly known for giving women orgasms (Hitachi... with the Magic Wand... if you're curious).
Prior generations were basically this way as well, using some custom setup based on popular components at the time. NES/SNES had a overclocked Commodore 64/Apple IIGS CPU, Genesis with a Motorola 68K like the Amiga, Macintosh and countless other machines. The Master System used a Z80 like on the Game Boy (also as a coprocessor on the NES and Genesis). And of course NEC with their own stuff codeveloped with Hudson Soft.
The point is that these wildly different architechtures lead to developers making different games for different platforms. This lead to what is often referred to as a second-party game. That is, a console/platform exclusive made by a third-party (think Square's run on the SNES or Electronic Arts on the Genesis). This is where most of the concepts of console exclusives come from. While the console developers themselves made a lot of games for their systems, they were still an overall minority compared to what third parties put out on their consoles in total. Even ports of the same game felt and played different on separate systems. For instance, I prefer Sparkster on the SNES compared to the Genesis, and Desert Strike on the Genesis compared to the SNES.
As an aside, taking into account the vast power (and cost) differences with PC, that was effectly a second-party only platform till about the 6th generation (considering there is no first-party since it's an open platform for the most part).
Long rant/post, but the point I'm getting at here is that as the consoles standardized, the concept of second-party games have slowly began to dissapear. This leaves only a handful of first-party games for each system with the rest being on whatever will run them from third-party developers. The only reason most second-party games exist today is more due to intentional platform licensing and not limitations. It's why the "just get a PC" meme exists: Because that's what you're effectively doing with both PlayStation and Xbox... with Nintendo of course insisting on being the outlier despite also using the same type of architechture as the most popular platform for gaming now: Smartphones.
A more entertaining/possibly quicker explanation than me in this video: