Badges are achievements. Reputation is a measure of their ability to help others in one expertise.
It seems that it might be useful to make the two more distinct by treating one's badges commonly across all stack exchange sites. This won't make badges and reputation orthogonal to each other, but will bring them out in relief against each other, and would provide a more interesting measure of one's expertise - both specific to a subject, and general to many subjects.
I don't think the same effect would be achieved by having this information appear, for instance, on stackexchange.com or some other profile aggregator. Having my SO account show both my SO rep, and my stackexchange badges would be a stronger driving force for me to work on badges as much as - or perhaps more than - any individual site's reputation.
The combined stack flair approaches this to some degree, but this type of change would be a fundamental shift in how badges are accrued, counted, and displayed, and honestly I'm not sure that it would be a good change, but initial thoughts suggest that it's worth considering and discussing.