Buried archaeology is not like artefacts, the act of renovation destroys some of it's essence, which is the potential to recover immeasurable amounts of knowledge from it and it's surroundings, and that's a lesson Archaeology has learned the hard way but very thoroughly over time and is committed to now (though detectorists aren't) – to the extent that 99% of excavation takes place only in advance of development and loss of the asset and the remaining 1% , for research, usually involves only sampling a few percent and leaving as much as possible for the future. To the extent that, other than maybe 1 or 2 stones, EH would certainly not agree to a grand project and most archaeologists wouldn't agree to take part in it.
In the light of that, TMA calls for not one but lots of unthreatened stones to be dug up look a bit out of line with modern archaeological thinking and maybe gives the archaeological establishment the chance to look down on amateurs, which is a shame.
A small point but well worth making is that 'amateurs' have often discovered and contributed to the knowledge of the science of archaeology. Not forgetting that archaeology needs a lot of manpower to excavate sites, (okay forget Time Team and its mechanical diggers); the contribution to our knowledge by small history societies and individuals in voluntary capacities should also be acknowledged.
The presumption that archaeology would be better in the future, is, after all only a desired wish at the moment, presumably soil analysis could be better in the future but read any archaeological report and they are very thorough even today.