Tackling the issue from a more verifiable data perspective - grading service population reports...
Here'a a quick look at the Missouri population numbers from Professional Coin Grading Service (PCGS). Numismatic Guaranty Company (NGC), ANACS and Independent Coin Grading (ICG):
TPG Service Plain 2*4 Total Plain % 2*4 %
PCGS 2,527 2,048 4,575 55.2% 44.8%
NGC: 2,031 1,662 3,693 55.0% 45.0%
ANACS: 437 228 665 65.7% 34.3%
ICG: 141 68 209 67.5% 32.5%
Combined, Plain = 5,146 (56.2% of Total)
Combined, 2*4 = 4,006 (43.8%)
Combined, Total: 9,152
These figures appear to support a fairly even mintage split, but a slightly higher mintage for the Plain variety. But are they a good proxy?
If the Plain:2*4 ratio found from the combined grading reports is applied to the net mintage of 20,400 (as reported by the US Mint), a split of roughly 11,465 for the Plain variety and 8,935 for the 2*4 variety is found. Does the near parity of these figures thus argue against a 5,000 mintage figure for the 2*4 variety? The evidence is mounting, but is it definitive?
Noted commemorative coin dealer and author Anthony Swiatek, in his book
Encyclopedia of the Commemorative Coins of the United States, published in 2011, suggests that up to 29% of the graded coins have been re-submitted. If we use a more conservative 25%, it leaves over 3,000 unique 2*4 coins - that's ~60% of the reported 5,000 mintage for the Missouri 2*4. A not unreasonable total, IMO!
Where does that leave things? It's hard to say. The expression "Clear as Mud." comes to mind.
There is undeniable value in first-hand market experience and acknowledge that astute long-time dealers develop a sense of surviving populations based on the number of coins that they see/handle. I'm also drawn to data gathered over the past 30+ years as presented via 3rd party grading service population reports. As data-drive as I am, however, it's difficult for me to simply disregard the mintage information provided by the coin's sponsor, the Missouri Centennial Commission, at the time of the coin's release back in 1921.
All that said, I'm inclined to think that the 5,000 mintage figure published in 1921 was under-reported - likely mistakenly - and that the Missouri 2*4's actual mintage is higher - the "
Red Book" may have it correct (or nearly so)!
(Of course, I'm just a collector who "dabbles" in US commemorative coins, not a noted dealer with decades of experience!)


For other of my posts about commemorative coins and medals, including more about the Missouri Centennial half dollars, see:
Commems Collection.
To check out Part I of this discussion:
-
1921 Missouri Statehood Centennoal - Mintage Figures? - Part I