Just be aware that when it comes time to localize to other languages it starts getting hard to support things like CJK where in order to properly work there's an Input Method Editor (http://i.imgur.com/JmmYwyi.gif) that needs to be able to read the text. There's also cut/copy/paste which users can't do from text on a canvas. There's also "define" which is built into OSX and iOS (others?) letting the user select a word and look up its definition in the dictionary. Finally I'm sure there are accessibility issues. And don't forget right to left like Arabic. (https://www.flickr.com/photos/u-e/2680759761/)
UI in a game (the most common place to render a UI yourself) usually doesn't care about these things. I'd hazard a guess though that most apps do. I know I get really annoyed when I can't copy small pieces of text from a native app. For example copying a link to a browser, copying a phone number to my phone, copying an address to maps, etc.
In general DOM makes all of these just work.