Investigate DOM restructure to avoid save/restore of transient state

[GerardasB]

Need to figure out what to do with i.e. panel collapse animations.

Similar problems/threads:
facebook/react#13042
reactjs/rfcs#34 (comment)

[raplemie]

With Popout now using reparenting, this does not seem like a suitable solution anymore given the scope of the work required to do that (and we would still need to keep the current reparenting for Popouts)