Sure there is a quality trade off, being jack of all trades but this industry is very elastic. You can have a great frontend engineer with only 2 years experience and an ok one with 6 years experience. Time in field doesnt really gauge skill well. Its more about the challenges one takes on and the variety of problems they solve with their code.
I guess most of the 90s and early 00s web devs were full stack then, including setting up the servers ("dev ops" I guess).
As the previous poster mentioned, it's quite simple, if you can implement a feature vertically (and I'm thinking at least a 3-tier system should be considered), you could consider yourself to be a full stack developer. I've met plenty of developers in my career who refused to work outside their tier.
The fact that sales people and recruiters are making full stacks up to be some sort of mythical horses with a single horn on their head is a different story...