I'm finishing my fourth year of a Ph.D. in mathematics. I have enough for a dissertation, and by the end of the summer, I will probably have enough for a very nice dissertation. And I plan to finish next year.
I also a couple of published papers not directly related to my thesis, and a few projects that might bear fruits maybe even this summer. So by October, when "application season" begins, I should be ready to apply to schools.
My advisor wants me to submit my work around the time I apply, so I can write in the applications that the thesis has been submitted. However, if I do that, I am likely to find myself without funding and without money for a significant portion of the year, as my university halts your stipend and employment as soon as your work is approved.
His argument is that a lot of universities might outright reject, or at least consider it less favorable, if I haven't submitted my work. As it might signal that I'm not ready to move on. This seems a bit odd to me. But I never sat in the chairs of those who make these decisions.
I also don't know how these things vary between departments, so I'm asking specifically for mathematics.