Add a clear field icon for <input type="search"/> in HTML

Unlike other browsers (Chromium, Safari etc), FF treats input type=“text” and type=“search” as same, so there is no clear field icon for search box in FF. Isn’t it good idea to make type=“search” consistent across all browsers? Indeed, using CSS we can easily add a clear field icon, but what’s the benefit of having two different input types with same behavior.

<html>
<title>Test</title>
<body>
<input type="search" placeholder="Search..." />
</body>
</html>

chromium-search.cleaned
Fig 1: HTML page with input type search in Chromium, with clear field icon.

ff-search.cleaned
Fig 1: HTML page with input type search in FF, with no clear field icon.

PS: According to HTML specification, primarily difference between input type “text” and “search” is style.