I almost wrote this same proposal myself as a suggestion a few weeks back. As someone who has invested a lot of time on several of the religion and culture sites, I'd very much like to be able to use that work to get more attention for my Stack Overflow questions. I'd like to think that the hard work I do over on my beloved Christianity.SE and Politics.SE should earn me the right to be heard better on SO. Indeed, the fact this has been asked before: Can there be an option to allocate rep from any site account for offering a bounty? really just sprurred me to think I need to write it up better.
The only problem is, they are right. Different sites are different worlds.
The "exchange rate" isn't nearly the same on SO as it is on Politics, Money, or Christianity. Here on MSO, for example, I was able to hit 1000 in a matter of days. On Christianity, I can pop that out in a week or two. On Money, it would take months. (And on Skeptics, I'd be tempted to wonder if anybody there believes it is either possible or worthwhile. But I digress.) That alone would mess up the economy - imagine if I scooped up my rep from a lucky break on MSO and put a 300 bounty on a Money question. Everything would get screwed up.
Moderation between sites would exponentially get harder. Not only do I have to look at the user's rep on my site, I need to look at all his sites.
The efforts to make one site great don't necessarily make other sites great. As such, no matter how much time I spend making SciFi better, it doesn't really add a thing to StackOverflow. Sad, but true. The reputation system exists to tell others how much you have invested in that site, not the network. If we were one site this would be wholly appropriate. But, for better or worse, the decision has been made that we're not.
And, as unfair as this sounds, the fact that I have earned the right to heard loudly on Christianity and Politics doesn't necessarily mean I have the right to be heard on SciFi or SO. Yes, I need SO for work, but I'm not Jon Skeet. I'm Michael. I'm good, don't get me wrong, but I'm not Jon. And I haven't really earned my chops over there.
So, long story short - I wish you were right. But, with deep thought, it is hard to make that case.