the dom is a mutable data structure and the native (fast) dom apis expose mutable interfaces. so dynamic sites (you know, single page html5 apps doing all sorts of client-side dom manipulation) are either going to be slow, or are going to have an imperative core, which is where you need functional programming the most ;(
maybe HTML6 will have native functional dom manipulation and we can rewrite all our favorite javascript libraries to expose functional interfaces. one can dream.
I'm afraid you're confusing data structures (such as vectors, sets and maps) with the document model object.
Not even in JS the DOM and objects are the same - some properties of the DOM have 'magical behavior' attached.
ClojureScript does not provide any functional interface to the DOM - that would involve a Haskell-like model of programming (monads etc), which Clojure programmers rarely do in practice.
there is ongoing research into dom manipulaton in clojurescript - Conrad Barski presented one approach[1] at Conj 2012 where the dom is mirrored in clojurescript data structures, and then 'synced' with the dom - so that way the imperative ickyness is tucked away in the sync method - it remains to be seen if that can be made fast enough until we get a native persistent interface to the dom.