What if a bug in Chrome (layout rendering, dom, ..) breaks your application? It's a corner case, possibly it will never happen. But this solution makes impossible for you to roll out a patch by just changing Chrome version bundled.
User will notice a bug in your application and maybe none of his frequently visited web-apps/web-sites exhibits the same bug, so you won't have the user engaged to update (or downgrade!) his Chrome version.
All in all you're breaking one thumb rule which is to use fixed versions of dependencies for your products, so to be sure they always work as intended. As a side note, how is one going to test a GUI build this way? Should it be tested against all Chrome versions that may be possibly installed at least at one customers premises?