I wrote my thesis with git + vim + latex. The main issue with collaborating like that is that you require other people to be able to use, say, git + vim + latex.† That may not be a problem for you and your colleagues. If it is however, Overleaf basically reduces it to "please open a web browser and have a look".
The other major argument is, of course, that you get an off-site backup "for free" for something as life-changing as your doctoral thesis, too.
†Of course, the other thing about having lots of local commits is that you can easily graph, say, words as quantified by texcount vs time and include the resulting diagram in the final copy of the document...
You're answering a different question from the one that the GP asked. What's the advantage of using overleaf over git + $EDITOR for a document with one author? Regarding off-site backups, that is already provided by your git host (github/gitlab/...)
The other major argument is, of course, that you get an off-site backup "for free" for something as life-changing as your doctoral thesis, too.
†Of course, the other thing about having lots of local commits is that you can easily graph, say, words as quantified by texcount vs time and include the resulting diagram in the final copy of the document...