If they get you using their browser they have complete visibility and control over what you do, whereas Google and Apple control the dominant browsers and subsequently what anyone else can build upon them.

Google has also locked-down default search engine on every major browser, including in at least Apple's case contractual obligation not to provide a search engine selection screen so they're fighting an up-hill battle for adoption there.

This doesn't allow for much and I think especially in terms of agent-control, for example IIUC Playwright and Puppeteer have always had to use modified derivatives of the main browsers for their automation.

it was chat-ui last year, vscode forks this year and maybe browsers are next.

I think they are also building an IDE too. It's just about control.

Data capture.

They can pretend to be humans when requesting content from sites, thus bypassing blocks by Cloudflare et al. The content can be then passed to the AI mothership.

They also get complete visibility over what you do, as @benouau says.

If I was them I would build whatever brings my product to more people

It’s not that hard.

Same reason as why Google built theirs.

Data being piped over to their respective AI flavor.

Plus, riding the hype wave.