Variance in coding style is a huge problem. Reading code where the style varies all over the place is painful. Moving code from one place to another and having to restyle it is awful. Constantly adjusting the style in which you're writing code to conform to the local style of the project, module, file, function or line you're modifying is miring.
Therefore projects adopt style rules to encourage and enforce a uniform style for the project's code. However, these rules still have to be learned, and adherence to them checked and corrected, usually by humans. This takes a lot of time and effort, and imperfect enforcement means code style consistency gradually decays over time. And even if it were not so, code moving between projects looks out of place because style rules are rarely identical between projects --- unless you reformat it all, in which case you damage the relationship with the original code.
I see this as a failure of language design. Languages already make rules about syntax that are somewhat arbitrary. Projects imposing additional syntax restrictions indicate that the language did not constrain the syntax enough; if the language syntax was sufficiently constrained, projects would not feel the need to do it. Syntax would be uniform within and across projects, and developers would not need to learn multiple variants of the same language. More syntactic restrictions would be checked and enforced by the compiler, reducing the need for human (or even tool-assisted) review. IDE assistance could be more precise.
Two major counter-arguments arise. People will argue that coding style is a personal preference and therefore diversity should be allowed. This is true if you only participate in particularly small projects, but if you work in a large project then --- unless you are exceptionally fortunate --- you will have to deal with a coding style that is not your preference, no matter what. (Maciej Stachowiak once said that willingness to subjugate one's personal preferences to a project's preferences is a useful barometer of character, and I agree!)
A more interesting counter-argument is that many coding style rules aren't sufficiently formalized so as to be machine-checkable, and might even be very difficult to formalize at all. This is true; for example, line-breaking rules or variable naming rules might be very difficult to formalize. So I relax my thesis to claim that at least those rules which can be formalized should be baked into the language.
(Figuring out exactly which rules can be formalized, and exploring alternative syntax designs that maximize automatic style checkability while still being nice syntax, sound like fun research! Programming language syntax is one of those areas that I think has been greatly under-researched, especially from the HCI point of view.)