First off, I want to say nice work on the research. A lot of people like to throw around opinions that are not based on anything besides their own illusions.
I also completely agree with you that the passing game needs to be more balanced.
With regard to your numbers, I think what you're clearly saying is that we don't THROW to our TEs enough - which is very different from saying we don't USE our TEs. In fact, we use our TEs quite a bit both as blockers and potential receivers. Why Brady chooses not to throw to them is not quite so obvious, but clearly the quality of the TEs as opposed to the quality of other receiving options has something to do with it.
I've done a little research of my own, and here's what I found. The number below represent the % of the team's total passing offense the TEs are responsible for - as Targets, Completions, and Yards:
2009: 10% of targets, 11% of completions, 12% of yards.
2008: 12, 9, and 8.
2007: 12, 12, and 10.
2006: 27, 25, and 29.
I couldn't go back to before 2006 because I couldn't find target stats prior to that (which I think is the most important stat). But obviously since 2006, we've had a very different composition of WRs, which accounts for the difference.