I remember native mobile apps disrupting the web, rather than the other way around.

The reason native apps disrupted web apps was because they were (all else equal) more performant, and had access to more of the device, and because companies drove users to using their apps because they could get more value out of them that way.

My take on it at the time was that native apps gave companies a way to reset their relationships with web users, and bring them into an environment where users had less control, and companies had more.