I'm against timed exclusives, I'm against third party exclusives that aren't actual co-production, and I'm against those where the business incentive of the deal is primarily to prevent competitors from having it, where an existing franchise fanbase is the primary value of the deal. It's partly a business ethics argumentation, which is forbidden here, so I won't. (but hey, we're allowed to call each other a bunch of butthurt crybabies, for some reason)
However, I really love first/second party exclusives and I respect third party exclusives that are co-productions.
The big difference is that one method is to add more games available to gamers, the other method is to remove offering to competitors. One is good for the industry and the other destroys it. Etc... This distinction is the center of disagreements.
I have lots of games that I still play for Amiga, PC, GameCube, Wii, WiiU, PS2, PS3, PS4. Roughly 80% of my console games are first or second party exclusives (it's practically 100% for Wii/WiiU). My PC rig is for games that aren't available on consoles, or games that are much better with KB/M, most importantly MMOs. Amiga emulator is for nostalgia and doesn't really count.
I think it's just that the type of games that I like are rarely the latest popular genre, and third parties need strong sales everywhere so they always go toward the popular genre.
The good reason for first/second party exclusives is that the console manufacturers can fill up the genres offering, spread it to stabilize the influx of games in a regular way. They can add games of a specific genre which is naturally ignored by third parties, even if it's not directly profitable, or more risky. The reason for them to make a game that's already popular genre is if they can do better than anybody else and provide differentiation (TLoU and Super Smash comes to mind).
I don't know if that's why Sony is winning this generation, but it works for me because they make the games I like. My PC is now mostly for MMOs, Nintendo consoles for Nintendo games, and most everything else is on PS3/4. This situation wouldn't have happened without the number of Sony's first party offerings, or Nintendo's unique ability to make games which have no equal anywhere.