Frank
I don't put this idea forward as a way of redistributing traffic from LHR to regional airports. I agree with you that it wouldn't have that effect. However it might make some regional services viable when they otherwise wouldn't be.
However I do disagree with you on the slot value point. I think it would reduce slot values, thereby making it easier for there to be churn between carriers. Fare levels are basically set by the market, so the only factor that would change is route profitability and hence the slot value (based on the premise that slot values equate to the net present value of the economic rent).
As for Shed's excellent post, while I agree with him in pretty much every respect I think we should accept that there is zero chance of APD being abandoned, and that the industry's focus needs to be on a 'fairer' structure of APD which maintains revenue to the Treasury. And in any event the linkage of APD to the environmental costs of aviation is a fig leaf that was abandoned many years ago. It's really just another form of taxation.