Dunno... I realise the weight issue made this unwise, but I can also see Voyager's point, actually... that boot was the first in all of human history to touch an alien world. There'll only ever be one "Apollo Boot", it would have been pretty amazing to see it in the Smithsonian, in the shadow of all those famous artefacts from the history of flight... of course, other man made artefacts (probes) touched the Moon first, but today we treasure and display items of clothing from ages past - suits of armour, war uniforms, crowns and jewelry etc - in museums, so The Boot would definitely have drawn crowds. I go to as many museums as I can, and would much rather see a genuine artefact than a photo of one, so I wonder what impression would have been made on kids since 1969 if they'd had a chance to see Neil Armstrong's dusty boot in the Smithsonian... so I don't think your idea is too outrageous Voyager.
But no doubt it will be recovered and put on display one day in the "Armstrong Musem" close to the Eagle landing site on the Moon itself, just as the boots of the first man or woman to set foot on Mars will one day be displayed in a martian museum, one gallery along from the , Pathfinder, MER and beagle exhibits, so its time will come, don't worry.