I don't think I cover the "full" stack, but I do much of it.  I don't do the networking or user administration for our company, or work on the website, written in Angular.  But I do most everything else.  There are two developers - or were; one left and we are working on a replacement - that maintain all the systems for our company.  I did the analysis with users to build a brand new system.  I designed and built the three main databases (200 tables, 150 functions, 550 stored procedures).  I am responsible for the business logic / object model that controls access to the database.  I did the major UI design for our Windows desktop application, half the coding, and am now the sole developer on that project.  I am the sole developer on the web API.  We had a consulting company create an enterprise data warehouse project, which I now maintain and extend.  I would like to know more about web development, but I have my hands full at the moment.  Our prior web developer left, so that is the position we are trying to fill now. 
As I say, that doesn't cover everything, but it does cover a lot.  I really like being able to see all aspects of the development process, from talking with our users to find out what is needed, designing and building the solution, delivering it (oh, yes, I do testing, QA, and deployment), and seeing the benefit to the users and company.  I've done consulting work in the past, and it was fun working on new projects all the time, but there I was doing one role over and over again.  Here I get to work in a lot of different areas, and shepherd a project from start to finish.  I prefer this kind of work.