Since Krakoa is now a nation, it should have an embassy, and that embassy should have staff of some sort, not just the X-Men team operating out of the treehouse.
A younger group operating out of one of these embassies might make more interesting (and telegenic / media-friendly) ambassadors, instead of older (more villain-y) folk like Harry Leland.
The mansion seems a bit away from the city for an embassy, but with the use of gates, it's literally a step away from wherever they have a gate, and they could even spin it as a deliberate choice to not put their embassy in the heart of the city where it would be a potential target for groups like Orchis and Xeno, and endanger the surrounding population.