Google recently implemented a fixed header design on their search engine result pages (SERPs). The header has an additional search field, which is competing with the already build-in search functionality in browsers.
This decision could very well be the worst web design decision in the history of Google.
I know from my own personal experience that fixed headers are hugely annoying to users, and thereby bad for UX. It can be done in ways it does not interfere with usability, but usually I do not recommend it. For the same reason I do not recommend having (any kind of) popup with close a button.
Popups are related to fixed headers, maybe even worse
For popups, the close button is usually made impossibly hard to hit on mobile devices. This is without mentioning the disruption it causes to the browsing experience. In the EU, GDPR creates a whole category of issues on its own, but often it also results in impossible-to-close popups. Sometimes you can not even accept those things.
Fixed headers can not even be closed, and so they tend to be worse than brief popups. Besides, you can choose to show popups only to loyal, returning users, increasing the chance they might respond to your message, and not be disrupted by it.
Bad UX and UI
I mean, they take a core service (search), and add a almost totally redundant fixed header, with no consideration of people using small screens. I also criticized this for webmaster tools (now known as Search Console), when they did the re-design.
As a user, I am really annoyed by fixed headers. Often, I find myself using plugins to disable whatever fixed elements web designers have plastered carelessly on web pages. It annoys me greatly, and I will not have it in my browser. Even when I am home at my 1920x1080 monitor, I still find fixed headers annoying.
In this case, the screenshot speaks for itself. It takes no genius to understand why having two input fields next to each other is bad. I am aware the address bar is not quite the same, but it serves the same function – and besides, I have no need or desire to have a fixed header on SERPs.
They could at least add a small button to close the header for users who are inconvenienced by it. Some browser plugins allow people to pick elements from the screen for easy removal. I think most well known ad blockers have this "feature". Although this feature was likely intended to block ads, it also works for fixed elements.