https://www.legion.org/moment-in-time/214460/out-55-american-legion-departments-how-many-have-post-1

They apparently sub-divided the nation into districts (not sure if it went exactly by state lines) and numbered posts independently of one another, seemingly because so many veterans wanted to form local posts after World War I. Other fraternal organizations like the BPOE/Elks preferred to keep a national numbering system, now going into the four-digits.