"Allow" isn't the right term at all. They would have to spend a lot of money for a team to reprogram all those games to work with the PS4. They have no incentive to do that, especially not this late in the life-cycle of the PS4.
Microsoft did it as a PR move because they were desperately trying to recover from the XO launch. Sony was never in that position and, to be quite honest, the fact that it didn't hinder PS4 sales probably indicates that it's not all that important to the average consumer. Sony going the Microsoft route at this point would likely do very little to increase unit sales.
If it was going to happen then it would have happened before now.
So, I guess that means then really that if we want the most out of our consoles, that it's better for them to be lagging behind other consoles because that forces them to have to do gestures of goodwill.
That's the way it's always been and it's true of most markets, not just gaming. In order to increase market share, businesses often try to one-up those higher in the hierarchy, which sometimes forces those changes to become industry standards.