With applications written in javascript ? Stateful on the client side alone or stateful on both sides ? It wont be safe to assume that state is persisted transparently on the server side. May be they just cache it for a while.
To make this work reliably would be quite difficult.
You could be really conservative: only assume statelessness if the page has no <form> elements and has no calls to the XMLHTTPRequest API (or window.eval).
Or you could be really conservative: only assume statelessness for pages without forms and without any Javascript. (These do exist!)
We have seen things people wouldn't believe. Webpages without any Javascript. Webpages using correct http responses. Watched C-beams glitter in the dark near the Tannhauser Gate. All those moments will be lost in time, here come the transpilers
To make this work reliably would be quite difficult.