That's not really a problem for Stagehand. It's a problem for Selenium, Playwright, Puppeteer and others at the browser automation library level.
It may become a real problem for the usefulness of this style of LLM driven browsing.
There are plugins that extend the major browser automation libraries to do this sort of thing.
And undetectable browser automation doesn't use Playwright, Puppeteer, or Selenium at all.