The 770 figure is absolutely false. 4 pieces of information should make it obvious:
1) Wait times can be up to a year in order to complete the renunciation process. Wait times would not be needed if only 770 people were renouncing
2) Renouncing is beginning to take up such a large proportion of embassy resources that the fee to renounce was raised 422% in one year ($2300). If a mere 700 people were renouncing the cost / benefit analysis to see if the fee needed to be raised would cost more than just leaving it where it was. In addition, there would be no reason to try to price people out of renouncing by making it unaffordable.
3) FBI statistics has stated the state department is clearly lying about their renunciation figures. The FBI has to also compile a list of renouncers which should only be a SUBSET of the list the state department compiles but somehow the subset continually lists more renunciations than the entire data set which the state department is supposed to list.
4) Other countries have statistics of their dual citizens who have renounced. One such country is south korea. Somehow the number of reported korean renouncers reported by the korean government is nearly the total of all renouncers as reported by the state department
As to why it is important? It is important because those who renounce are oftentimes the type of citizens the US wants to attract. Expelling these people will likely not serve US interest. Especially because after renouncing these people more than likely no longer function as ambassadors to the US whereas they would probably serve that function before. Just look at the mayor of london and he has not even fully renounced yet!
None of these wild speculations "prove" anything.
The fact is, every year, hundreds of thousands of people would immigrate to the USA if they were allowed to.
Even if the 770 number is wrong, its still only a few thousand people per year that renounce.
A tiny fraction of these are Mosquito Coast type anti tax conspiracy nuts- and the rest are mainly two categories-
1- American citizens who marry foreign nationals, move abroad, and want to fully become citizens of their spouses countries
2- People who have immigrated to the USA, and decided they didnt like it, and return home.
Historically, both of these instances have always happened.
In fact, historically, it was more like 5% to 10% of all immigrants to the USA that returned home- including Irish, Italians, Greeks, Finns, and, of course, Mexicans.
Many, many mexicans and other central americans work for 20 or 30 years in the USA, building homes brick by brick back home in Mexico, and, when they retire, return to Mexico, where its much cheaper, and they already have a house.
This accounts for a lot of these renunciations- they become US citizens, because, obviously, its so much easier to function in the USA as a citizen, but they still return home and have always been Mexican.
http://www.nationaljournal.com/next-america/policy/why-immigrants-boomerang-to-mexico-20140117
http://www.thefiscaltimes.com/Articles/2012/05/14/US-Educated-Immigrants-Return-to-Their-Homelands
if you do any googling at all on this subject, you find that there were times in US history when 50% or more of immigrants returned to their home countries.
Using the logic of some posters above, regarding rate of Increase (or, in reality, DECREASE), you could easily surmise that, soon, the USA will be completely devoid of humans. In fact, this is obviously not true,and US population is steadily growing, primarily due to incoming immigration, not shrinking due to fleeing the Kenyan Marxist Usurper and his jackbooted IRS