To answer the main question, console exclusives (which for the most part are first party games) have always been good for the consumer, it ensures that each console developer takes the time to entice gamers with worthwhile experiences you can't find elsewhere. Once they have their attention, they need to make sure they retain that interest with additional exclusives. This perpetuating interest is all backed by a high quality piece of hardware that can run the said exclusives as seamless as possible.
If you take away the exclusives, all you have left are third party companies spending more resources on coding each version to work as smooth as possible for each platform, which given past track records for multiplats (like Skyrim and Silent Hill HD collection, for example), isn't always effective (even post-patching). This same effort can be put towards making one definitive version compatible with one set of hardware rules, and creating a more fleshed out experience in result of this.
In short, if there are no first party exclusives to bring to the table (which be honest, why would Sony / Microsoft / Nintendo want to sell software to consumers that own the competitor's hardware, when they currently have an existing hardware model that they need to sell?), it would decrease the competition and quality in the current marketplace, and would overall hurt the gaming diversity available.
If you are talking about a future system where there is only one hardware box available, and that all but one company gets out of the hardware game, then who would be the one company that would dictate the hardware? That idea is too similar to the current PC marketplace, which is basically where most all of these ideas have already been streamlined anyways.