Maximum, my company SOPs don’t give that option unless the WX at the destination is above certain viz/cloud base requirements, there are two separate runways and there are no untoward ATC delays expected (that might get you into your final reserve).
I’m quite happy to do what you suggested in this situation, (and have done at LHR), but (and it’s never happened yet) if I don’t look like getting on the ground with all my final reserve intact, I will not hesitate to declare an emergency. Commonsense should dictate that you give ATC a ‘heads up’ at least 10 or 15 minutes beforehand to warn them of the time at which your pucker factor reaches Warp Factor ‘x’. I’ve discussed this situation with colleagues, some of whom seem remarkably unfussed at what I see as a potentially serious situation, particularly in such a busy environment as the LHR terminal area. Call me a wimp – but I hope to get to be an old one - (and ‘dogmatic’ is a criticism I’ll quite gladly suffer when it comes to fuel.) I am paid to get my aircraft and my passengers on the ground safely, (preferably at destination), not to put them at risk on (perhaps) tenuous judgement calls perhaps clouded by commercial factors.
If I may labour the point: min diversion fuel and whether you are going to accept the second runway as an alternate (if you can) should be discussed to detail before top of descent as part of the approach briefing. Both pilots should agree on those figures whilst still in the cruise, and as far as I’m concerned, after that, they’re damn near set in concrete. Whilst I agree that a small amount of latitude should be available in the situation where can see you’re next cab off the rank and both pilots are happy to press on, I hold the very strong opinion that below 5000’ in the terminal area is NOT the place to be discussing and amending your minimum diversion fuel.