"Every airline doesn't need their own webpage. They could all provide a standard API."
That's sort of how it works in the corporate booking tool world. It is decidedly not a better experience for end users, IMO.
There's quite a lot about each airline that is different, so any unified approach is a lowest common denominator. You'll notice things like loyalty points, for example, have more rich data on the airline's website. And that some fares are ONLY on the website. Or that seat maps have more useful detailed info, etc.
And that's all shopping/booking. Departure control, flight status, upgrade/downgrade, check-in, seat upgrades, standby, etc, are for the most part only on the airline's website.
Every airline doesn't need their own webpage. They could all provide a standard API.