PhD student hiring a LaTeX expert to typeset thesis?
(I will quote a comment by kahen and a chat message by Ulrike Fischer.)
You have got three qualities of the thesis production: good, cheap, fast. You can choose two.
Hiring a LaTeX specialist is good (if you find a good one), fast (if you find a good one) but expensive --- typesetting a 100-page thesis can take around 20--30 hours of work, easily more depending on the text, on the person you work with, on the amount of discussion about the appearance, proofreading etc.
Making it yourself is cheap. However, unless you are Jarod from the Pretender series or you know LaTeX already, it cannot be both good and fast.
Of course, making it yourself is better in moving your LaTeX skills forward, but I do not think this is crucial for an academic career, surely it is not more crucial than submitting a quality thesis in time. People hire services of all kinds, you get grant-writing, typesetting, conference organization, IT, etc. --- very various kind of out-sourced services for which someone can say: "A good researcher has to be able to do this."
To answer your question about LaTeX services: I doubt universities have, in general, such services themselves. Some have a LaTeX theses class (of varying quality), some even do not have this. However, there are independent LaTeX consults and consulting companies. I can't list any since (1) I don't know them and (2) this is not an advertising site. However, remember that these people are highly specialized, and the prices of their services reflect this.
The best thing to do would be to practice it yourself and code with the help from forums such as TeX-LaTeX at StackExchange. If your school/university provides the class file for LaTeX formats, then more than half your thesis compilation work is already done for you. The Wikibook on LaTeX is a great start and should have nearly all you need to start typesetting your thesis in LaTeX.
As my University didn't have a standard thesis class (at that time) I had to come up with my own class file for my masters thesis by deriving it from the existing thesis.cls class file. It may take a bit of work for a week or two. But it really pays off at the long run. I never thought typesetting a thesis would be much simpler. I had a much easier time than my colleagues who used Word and was very easy to make from the very minute to the most complex changes without affecting the perfection of the formatting. It is what LaTeX is all about: focus on the content and not the formatting.
This is a bad idea, as others have said. Instead I'd recommend a very simple copy-and-paste job by yourself. Once you have a template configured (I'm using arsclassica, for example), writing LaTeX is for the most part just plain text; 90% of your thesis will copy-and-paste over without incident. Of course, the remaining 10% (tables, references, equations) will be more painful but after a few hours you'll have a great looking document and a decent life skill.
An alternative is to try an online LaTeX IDE like overleaf (formerly writelatex) which some seem to prefer. I wouldn't recommend desktop LaTeX WYSIWYG editors, if you have all your content prepared I'd imagine such an approach would be more of a headache then the copy-and-paste method.
Finally, as yo alludes to, many academics do just fine producing horribly-formatted documents, posters and presentations — it's the content that's important afterall.