Why do journals reformat your submissions?

I can think of a few different reasons:

• Not all authors are able or willing to conform to the formatting style. After all, academics are supposed to be experts in their field of research, which usually isn't typesetting. The journal provides formatting as a service to these (and other) authors, and to ensure a consistent style.
• Copy-editing can also fix a number of typos - it doesn't always just introduce errors...
• Even if the authors manage to nail the formatting and spelling, chances are that the journal has an extensive style guide that goes way beyond "some additional rules". If you submit papers to more than a single journal, will you really be able to remember which journals insist on capitalizing words like "ansatz" in English?
• Additionally, journals may use headers/footers they don't want to make available in public templates, or even unusual page sizes that may require the text to be reflowed.
• Publishers may accept manuscripts in several formats, and have to convert at least one of them into their own format of choice.
• I don't know how common it is, but the format of choice need not be one of the accepted formats at all. E.g. APS accepts LaTeX and MS Word submissions, but converts both into an XML format. This allows them to generate both PDF and web versions of the papers, and additional versions in the future. There is even work underway on using the XML format to make papers fully available to the blind.

Finally, as long as the author signs over some or all of their copyright, such issues should not be a reason for this. Also note that formatting/editing does not necessarily cost that much, especially compared to carefully checking a submission.

If all authors were able to produce camera-ready manuscripts, publishers would not need to reformat submissions. The problem is, most authors are not able to do so (including those that think they are).

If you've ever reviewed articles before you'll probably have seen what un-typeset articles journals deal with. They can look fine, but they can also have figures separate from the article proper, text overruns, broken references, and misrendered equations. I've seen papers submitted using another journal's style files, which is still fine as long as there are typesetters who can reformat the manuscript. I've also seen papers which had missing paragraphs, but on checking the source files the paragraphs are there, they just did not compile right.

TeX makes things easier but still isn't foolproof. I remember one author sending me an angry email saying "I've sent you the files, why can't you just press print? Doesn't LaTeX do all the relevant typesetting?" and I showed him a page where LaTeX put the figure on one page and the caption on the next.

Don't get me wrong: if you prepare your manuscript well, the typesetters have less work to do. You're right that sometimes reformatting introduces errors, but the number of errors removed is significantly higher than the number of errors introduced. Reformatting manuscripts is significantly more expensive than handing CRC manuscripts. But even CRC manuscripts have to be checked.

To supplement the excellent answer by @Anyon:

• It might be not desired for third party to produce something in exactly the journal look. From what I have seen, even the "non-review" modes of journal styles often look different enough from the actual publisher-made final version. Basically, an officially-looking copy should originate only from official source.
• One further reason might be the fonts. Proper fonts are a big deal, they might cost a lot, and they would typically not be available for the normal user.
• It could be that final processing happens with something different, as mentioned in the above answer. One possibility is that they reformat the columns with InDesign or similar that is believed to achieve a better journal look than LaTeX. End users would obviously not have unlimited access to such software.