Sort of looking at this from another perspective, but aren’t we moving right back to the dumb server/ smart client scenario of yesteryear? You know, where big mainframes were serving raw data up to the client’s GUI program? Was there even this discussion back then? Maybe there shouldn’t be now?
Because, it is simply evolution, even if we are moving back to that mainframe type of computing, with the evolutional difference being the crazy scale the Internet adds to the picture.
So no, I don’t think today you can be a “full stack developer”, because if you are or try to be, then you are a “jack of all trades - full stack developer” and you are in pretty much master of none. If you are, you are the rare sort. The technologies evolve too rapidly (and not only on the front end either), which makes it difficult to be even a master of one.
In Germany there is a fantasy animal that describes a “full stack developer” today. It is the “eierlegende Wollmilchsau”. Instead of trying to explain it or translate that animal in words, I’ll let a picture explain.
There is no such animal!