Well I think it's more an opinion than fact - what possible power could have been lost if Diana stayed alive? Embarrasment, Scandal and Media Rubbish yes, but a loss of power? No. I think you overestimate the power Spencer had. Again, my opinion.
It's not that Diana had power. It's more that she knew things. You can't spend 16,17 years in the British royal family (for even divorced, she was still at least half-in due to her sons and living in KP) without knowing secrets. This is not to say there were definitely secrets worth guarding. This is just a very compelling possibility when you consider that governments and royals, celebrities and wealthy people (in short, powerful people) often go to extremes to protect some secrets. I'm not personally a believer in these conspiracy theories around the crash. I am, however, open to the possibility, because let's face it. Stranger things have happened, and if Diana was killed because of some secret(s) then her killers should be brought to justice. I don't believe the royals themselves had anything to do with it. the ones under my suspicion are more the people who have a lot to lose if someone like Diana learns too much about something, threatens to reveal it, or gets too close to enemies of the Establishment. We all know Doda's father had/has enemies! These are people behind the scenes, the people who turn the royal wheels, the intelligence agencies who spy on them.
You said let the weirdos pay for it........ Frankly, I think a private investigation would be more productive than a taxpayer one! Let Fayed pay for it. He might be shady, you might not like him, but least his investigators would be private, have no loyalties to any national agency. In this way, it would be objective, supposedly.
More objective than Scotland Yard could be. Nothing against Scotland Yard. I'm sure they're a fine agency, but it's a fact that they have loyalties in people who could not possibly be objective.