One could point out that the Lenin Mausoleum is still in Red Square and is still visited by members of the public-perhaps not as many as before 1991 but still a goodly number. Putin is publicly on record as being opposed to its removal and the burial of Lenin's body.
Indeed, but the Mausoleum is only open two mornings per week now - and its visitors are almost entirely gawping tourists, rather than fervent Leninists ;)
It's a much 'easier' tactic to wind it down slowly, than shut it down and rebury its sole occupant (as, ehem, Lenin requested in his Will - for a private burial alongside his brother). "People I know" have confided that keeping Lenin under watchful eye on Red Square is a kind of safeguard against having a tomb elsewhere ransacked or desecrated.
Of course, the tombs of the other USSR leaders (except Khrushev) are also part of the mausoleum complex, although they are not mummified as Uncle Ilich is - they are mounted behind the mausoleum. There was also a tradition - connected, primarily, with arranging ceremonial burials in a secular society - of burying the ashes of Heroes of the USSR in niches in the Kremlin Wall. There's a little "Avenue of Glory" behind the mausoleum, and adjoining the wall, where you can find people like Yuri Gagarin, and American communist John Reed commemorated. Frankly I would not like to see Gagarin reburied elsewhere - his tomb belongs where it was placed by the people of his era, I feel? So removing the mausoleum opens up several other issues.
The thing which DOES irk me is that the magnificent building on the corner of Manege Square and Red Square (by the Chapel of the Iverian Virgin) is currently empty. It was the seat of the Duma (the Tsarist-era Parliament) in the C19th, and then after the Revolution it became Lenin Museum No 1 - "number 1" of many, since every town or hamlet had a Lenin Museum too... some were sadly laughable in their display material. This building ought to be put to some proper use - but the Putinites are too cowardly to grasp the nettle and throw out the rubbishy old displays about Lenin. It's been locked up for about 25 years now - a testament to the stagnation of the Putin years. It should clearly be handed over the History Museum, which stands adjacent, and hasn't nearly enough space for its displays.
(Or of course they could turn it into an opera house ;) )