Who's "we", though? Here's the list of Linux Foundation members: https://www.linuxfoundation.org/about/members It's a foundation by, and for, commercial interests; not the users. If the same interests made up a foundation to develop a browser, it wouldn't be different from Chrome; because in the realm where browsers are supposed to work, those 'commercial interests' would demand doing what Chrome does.
It's a 'happy accident' that with respect to a unix-like OS kernel, the interests of the industry ended up being compatible with the interests of the user.
Smaller browsers built on webkit do exist; see 'Epiphany', 'surf', 'luakit', and 'Nyxt'. Qt's web component used to be based on webkit as well, though they've switched to Blink (Chromium).
Unfortunately, none of the browsers listed above are 100% sufficient to replace Firefox. They all rely on GTK bindings on webkit, which has its own quirks; and none have support for webextensions.