Did Iron Age people see these monuments as representing the old gods who were not quite obsolete, as something to respect so as to placate vengeance from the past. Or perhaps did they want to harness supernatural protection for their fortress by retaining the ancients (literally) within their home. Or perhaps even to assert that 'this is ours, always has been... I mean, look who we've got living here?' Questions, questions, questions.
Yes, it's true that there are plenty of examples of cairns, etc left intact (for example the cairns inside the Clwydian hillforts of Penycloddiau and Foel Fenlli). But I'm not so sure that this was the case everywhere. Perhaps I need to come up with some examples though! As ever your post makes me question things I have thought previously.
The idea of IA people using the presence of earlier burial monuments to assert or valdate their "ownership" is interesting isn't it? In previous decades, this would have run contrary to the old "diffusionist" ideas that suggested this big wave of a so-called Celtic people invading Britain and briging their iron weapons and hillfort ideas with them. Not so now. So, there is certainly much more evidence to suggest that they were, largely anyway, the same "people" as the ones buried in their midst.
Alternatively, there are plenty of examples throughout history of invaders re-writing (pre-)history to legimitise their presence in an invaded country, so I guess it could be an equally possible reason for leaving the older monuments in place as proof of a "continuity" that was in fact entirely fictitious. Fascinating stuff anyway.