It really depends on what you call new.
I left in 2006 after 22 years and I did move every 3 years and that includes 12 years overseas.
In recent years (last 20 years) the transport fleet and indeed the rotary fleet have tended to be situated in one or two certain locations only.
Where as the FJ fleet have been based over numerous locations and therefore PMA have more options as to where you may be needed.
I agree that as of late the FJ options are narrowing also but I stayed on type for my whole career and still moved continually.