Firefox for Android is my primary browser on my Nexus 5 now that the AOSP browser has been removed. On my Nexus 4, I rooted the phone to get back to the AOSP browser, but when KitKat came out, it broke root. I haven't gotten around to re-rooting either phone.
And no, the "view in desktop mode" toggle in Firefox for Android almost never works. I've considered rage-reporting bugs for all the URLs it fails on, but it's an idle fantasy right now. It clearly isn't a priority for Mozilla.
I haven't seen it fail, but I have only used the desktop view when coming from a page that then gets redirected to a mobile page. Firefox handles that well.
Have you tried Firefox for Android?