Almost all Emperors were stationary or the marines knew where they were (WB, for example).
But even if: you have at least six immortal guys you can send anywhere to search for a number of top tier to posses; why not? Even now, Teach has a main base, Shanks sooner or later returns to Wano, etc.
No they weren't, Whitebeard lived on a ship at all times, sailing around. The Marines had people watching his ship leading up to Marineford but then he wiped them out.
Shanks also sails around and does not stay in one place.
Kaido stays on Wano a lot sure, but it's designed to be uninvadable, that was a huge plot point of Wano and why the Gorosei stopped the invasion after Momonosuke decided not to remove the walls and he does leave it to do other things like I already said.
Big Mom is the only real example of a person who stays in one place at all time, but that's in an entire country she controls, a Gorosei can't just waltz in lmao.