I like the idea of making reputation data available to everyone and let them run their own calculations however they want. Unfortunately (or fortunately if you're wary of the privacy implications), most online applications that have some notion of reputation don't share reputation data don't allow you to just grab the whole database.

A team's reputation does not need to involve divulging personal information about its members. Although, if a team is small enough, there's a good chance that generalized transactions reported between teams may still be matched to a particular team member.

The bigger picture is that a team in the proposed system would not have to constantly worry about funding, since it could use its budgets directly as currency as long as the team maintains its reputation. I think that for most participants that is more than good enough trade-off to take on small privacy risk. In other words, would a team rather worry about funding or privacy, and with good platform design those concerns might not even be mutually exclusive in most cases.

With regards to not having access to reputation data from online applications, there are work-arounds. For example, tweets, blog posts, or product reviews about a team could be crawled for sentiment detection and used in reputation metric calculations. These work-arounds might seem difficult to do, but so was search engine technology in the early days of the web.