To begin with,I do think that the restoration of monarchy in Russia could be actually one of the last needed things,but certainly not the least one,the form of constitutional monarchy being very appropriate,but I very much doubt it ever happens.The active groups who want monarchy back are mainly based on religious beliefs and predictions and they do not have any concrete figure of appropriate Tzar.Of course there are the others more concrete,but most people are indifferent.
The legitimacy of actual heirs is quite disputable.After Nicholas II abdicated,the heir was his son Alexei.But Nicholas abdicated for himself and his son(dubious).Next in line was his younger brother,Michail.He said he would rule if the people wanted him to,they didn't and in result he abdicated.The first Communist leader,Vladimir Lenin,was a perfect jurist and after ordered killing Tsar and his family he knew very well that there is no direct heir and would be a lot of confusions,as far as the female primogeniture(from Nicholas's sisters) was never accepted by Russian laws and the Nicholas's only brother Michail had a rather scandalous marriage.
Nicholas's cousin,Grand Duke Cyril Vladimirovich ,then proclaimed himself the Head of the Imperial family.Here the dispute began.For example,there was a question of legality of his marriage.He didn't have the approval,he and his wife were banished for a time.Of course they were eventually allowed back.His descendant is GD Maria Vladimirovna.The other Romanovs do not agree and dispute her claims.
I think Russia doesn't want them back ...but the one who seemed to have the most chances is Prince Michael of Kent,who actually speaks Russian and understands very well Russian affairs and reality.Of course this is more or less utopia.
In addition to all, these were old rules of succession,now Russia changed and the rules of succession could be regarded differently as well.The descendants of sisters of the last emperor of Russia are taken into account as well.The situation is rather different from,let's say,the last king of Romania,Mihai,who has living descendants.
Besides this,the sister of Nicholas II,Olga who lived her last days in Canada,her son Tihon Kulikovsky Romanov and her grand-daughter Olga Kulykovsky never accepted the GD Maria Vladimirovna and her son Georgi as the potential heirs.On one of her last visits to Russia,Olga Kulikovsky said that she could accept the others ,but not Grand Duchess.
Of course the most important are not disputes ,but the desire of people to see the Romanovs back on the throne.GD Maria Vladimirovna with Georgi participate in many official events,but they did not try to get closer to the people,to participate in some humanitarian projects or to open some study grants for gifted students.The people only know about Georgi's affairs with Nornikel and participation at many gala events with a lot of gloss and caviar.That is why many people who know about them,do not accept them as heirs and prefer more others or nobody.
Line of succession to the former Russian throne - Wikipedia, the free encyclopedia
Pauline Laws - Wikipedia, the free encyclopedia
Alexander Palace Time Machine - Romanov and Russian History