The importance of a person's Ph.D. thesis per se for their further academic career varies wildly, because the thesis is just one component in a person's portfolio. The significance of that component depends strongly on their intended direction and the contents of the rest of the portfolio.
First and foremost, remember that most people who obtain a Ph.D. do not end up becoming faculty at a top-tier research university. If your ambition is to end up in a more teaching-centric position or in industry, then research work is mostly just evidence of one's necessary technical competence. The primary work that such a person is hired for is almost never directly linked to their thesis: in a teaching post you may continue that research, but that is secondary to teaching; in industry you are probably going to end up working on something different, but that will exercise similar technical skills.
Even for those who do aim for a career of self-directed research (e.g., tenure track faculty), however, the thesis is only one part of the more general research portfolio. In some fields or for some particular people, the thesis is the key point of contribution, standing above all of one's other work. For many others, however, either the thesis is a compilation of results that have been achieved and published along the way, or the thesis is only one piece of a greater body of work. It is often the most important because others may have the person as a secondary contributor, but across all fields it is rarely the only significant piece of work.
Moreover, the next step after a Ph.D. is typically not faculty but postdoc, and it is one's ability to "flower" and become well published as a postdoc, with more self-direction and outside of your home laboratory, that is often a much stronger determinant of faculty hiring.
Now, if you write a bad thesis, it will most certainly be a detraction. In general, however, I would say that for most people in many fields, the Ph.D. thesis should be viewed as having an importance only equivalent to 2-4 major papers.