Sorry, but I have to say non-exclusivity sounds like a really stupid idea, as the market would most likely end up with a monopoly with consumers suffering. Think about it, if consoles had no exclusive titles, then you're going to pick the one which has the best quality and features for the best price.
Problem is though, because each console is going to have a different build with different add-ons, controllers etc. you and your friends are most likely going to choose only one to do most of your gaming on. This way you don't have to mess around and get pissed at the different quality or features or whatever each time you play at someone's house; you'll want to have a similar setup of play so you feel comfortable and can get on with enjoying the game. Ditto for playing online; having a mixture of different consoles would make it more likely that something will go wrong in interfacing and playing games.
The problem with non-exclusivity is that one console and developer will most likely emerge as the clear winner and the other two will bomb, and trying to convince shareholders to back another console with effectively 2/3 chances of failing hugely will make those two that fail pull out of the market as they can't afford the risk. So you end up with one company as a monopolist, free to ramp up prices and release more samey own-brand games knowing that consumers don't have any other choice. And the only way a company trying to enter the market would be able to compete against a monopolist would be to offer that very same exclusivity in what the gamer can play (or else spend and risk much more on an industry-changing gimmick that you hope will tempt consumers enough to make up for even more costs. Exclusive games would be a much safer bet.)
The funny thing is, the Big 3 know this, and they know its much better to play safe with exclusivity, where all are likely to make at least some profit, even if certain consoles only do well later on, than take an all-or-nothing gamble with non-exclusivity. Having the competition actually benefits both consumers (with better choice and not being held to ransom by a monopolist) and producers (in being much more likely to turn a profit).
Problem is though, because each console is going to have a different build with different add-ons, controllers etc. you and your friends are most likely going to choose only one to do most of your gaming on. This way you don't have to mess around and get pissed at the different quality or features or whatever each time you play at someone's house; you'll want to have a similar setup of play so you feel comfortable and can get on with enjoying the game. Ditto for playing online; having a mixture of different consoles would make it more likely that something will go wrong in interfacing and playing games.
The problem with non-exclusivity is that one console and developer will most likely emerge as the clear winner and the other two will bomb, and trying to convince shareholders to back another console with effectively 2/3 chances of failing hugely will make those two that fail pull out of the market as they can't afford the risk. So you end up with one company as a monopolist, free to ramp up prices and release more samey own-brand games knowing that consumers don't have any other choice. And the only way a company trying to enter the market would be able to compete against a monopolist would be to offer that very same exclusivity in what the gamer can play (or else spend and risk much more on an industry-changing gimmick that you hope will tempt consumers enough to make up for even more costs. Exclusive games would be a much safer bet.)
The funny thing is, the Big 3 know this, and they know its much better to play safe with exclusivity, where all are likely to make at least some profit, even if certain consoles only do well later on, than take an all-or-nothing gamble with non-exclusivity. Having the competition actually benefits both consumers (with better choice and not being held to ransom by a monopolist) and producers (in being much more likely to turn a profit).