At the moment, AI can't reliably deliver aesthetics, performance, security, and accessibility in frontend code.
But in the future I would say yes, there would still be value in tests for an AI-written codebase.
Why? Because for its human operators, separating "Is the application working correctly?" from the application itself will still be highly useful, even with advanced observability and monitoring tools.
Another way to frame the question is would you rather have an AI- written codebase with 0% test coverage or an AI-written codebase with 100% test coverage?