How important is the write-up of a PhD thesis for an academic career? How important is your written PhD thesis for an academic job search, assuming the results are already written in papers? Do search committees ever read your thesis in addition to your papers? My PhD advisor said that the written thesis is not important and I can write whatever I want as long as it's not about Star Wars.
Your thesis and what is written about it your letters of recommendation will have a big effect on your career initially.  To get a good postdoctoral position, you'd better have a good thesis.  Later in your career, your thesis won't matter much any more, because people will be more interested in your recent achievements.