I appreciate where you are coming from with regards to not being able to nominate your destination as an alternate when the weather is poor and Heathrow Director, you are absolutely correct that there would be no point in nominating LHR as the alternate if the weather was poor as you would definitely require an alternate (ie other airport)
However, I just think you could hugely reduce your fuel costs over the cost of a year if, when, and only when, the weather and conditions are suitable to nominate LHR as the alternate. Gulfstreamaviator seems to think along the same lines as myself.
Grasscarp, if your destination (ie LHR) was to close then a decision on a diversion would have to be made very promptly. You would still have half an hour of fuel remaining; at least. If, at the planning stage LHR was looking a little dodgy then of course you would nominate another (separate) airfield.
I still can't see the major problem with the suggestion. On a day like today I can't see any reason why it couldn't be done. The weather is beautiful and in the absolute worst case scenario you still have 30 mins fuel remaining for an emergency.
If it is not permitted, where is it written down?