Not at all. It is perfectly possible to go from a big freaking desktop app (BFDA) and rewrite it, piecemeal, to be a single page web app.

The way you do that is that you first, piece by piece, split the BFDA into multiple layers, then you make it client-server, split the data-storage into its own server, split the gui of, split the business logic of. Then you rewrite the parts that request stuff for the client into using JSON and rest, then all you have to do is to port the (hopefully) tiny amount of gui interface the user needs to Javascript and the entire app still works.

Is it easy? No. Does it waste some work? Yes.

What you're really giving up on is conceptual integrity. Some developers find it very distasteful to have an application that is only partially composed of a newer architecture, programming paradigm, whatever.

A few years ago I stopped an impending complete code re-write and a fellow developer was aghast at the very idea of supporting an application that was "only half MVC".

Not necessarily.

You can replace parts of an application with webservice calls, for instance.