The problem is that we're not starting from scratch - we have a web engineered for browser use and a world engineered for humanoid use. That means an agent that can use a browser, while less efficient than an agent using APIs at any particular task, is vastly more useful because it can complete a much greater breadth of tasks. Same thing with humanoid robots - not as efficient at cleaning the floor as my purpose-built Roomba, but vastly more useful because the breadth of tasks it can accomplish means it can be doing productive things most of the time, as opposed to my Roomba, which is not in use 99% of the time.
I do think that once AI agents become common, the web will increasingly be designed for their use and will move away from the browser, but that probably take a comparable amount of time as it did for the mobile web to emerge after the iPhone came out. (Actually that's probably not true - it'll take less time because AI will be doing the work instead of humans.)