I think there's a psyop aspect to it as well. Moscow was already heavily, heavily defended by AA but most of it was aimed at infrastructure and government (Kremlin/Putin/Etc) protection. Forcing AA assets to defend wealthy neighbourhoods is definitely a drain on Russian capabilities and speaks to a pretty deep understanding of how their regime works. Putin & the oligarch class hold each other up.
Cause frustration with Putin in the oligarch class and you start to create the conditions needed in Russia for internal regime change.
It has been said the Ukes are trying to leverage poor social cohesion in Russia. They are specifically targeting the oligarchs/insiders and studiously avoiding worker bees (whose sons/husbands are getting killed in the war anyway.)