The correct element to handle single-line text inputs is <input type="text">, however its default behavior for overflowing text is to make the field "invisibly scrollable". This has awful usability if the text tends to be longer, because the user cannot see the entire text at once and there's no scrollbar.
This leads to authors defaulting to textarea even if they want to preserve the the "single-line" input type.
A notable example of this is Google Search:
You want to allow long input, but also you want to preserve the ability to submit text with Enter.
The field-sizing proposal is another key of this puzzle, also seen on Google Search.