The sizes of the Dime, Quarter, Half-Dollar and 38mm Dollar were standardized for .900 Silver content around 1836-37, there's no reason why circulating cupro-nickel coinage has to adhere to these sizes.
Since we have had a 26.5mm Dollar coin standard since 1979, it would make sense to establish a 30.5mm Two-Dollar coin standard (now that the Half-Dollar is really gone from everyday circulation).
38mm circulating coin? Based on the above, it should be a $20 coin!
Any coin that big should have some real purchasing power, and Morgans sure did in their day ($1 in 1904 = $23 in 2008!).
A lower-mintage (say, '10 million per year' base target figure) 'limited-circulation' by design but still business-strike $20 coin would appeal to the gambling industry (as 38mm coins always did), and have undisputed collector appeal! Lower mintage by design would help quality control, boosting collector appeal. The high face value would make the coins
very profitable, even in their specified lower volume production runs.
The lower mintage target would make it more practical to distribute most/all of the run via 'Direct Ship Rolls' as a 'limited-circulation' issue (so they would NOT be sent to the Fed branches!). Any banks or casinos wanting the coins would order them directly from the Mint. If collectors gobbled them all up,
that wouldn't be a problem for the Mint, because of
seigniorage.
It might be wise to stagger the shipment dates (once a month) so they didn't all sell out in January.
Unlike A.S.E.'s, you could spend them for fun, use them at the poker table, and it would be a real treat to get one from circulation!

I'm thinking of a coin that would be 'limited-by-design', but something that could still be used in circulation (cupro-nickel business strike, matte fields on the flat surfaces, a simple design that would 'wear' well ie. an updated Liberty Head), and not a 'rarity' (enough made to keep them obtainable at face value, but
not dumped by the zillions into the Fed!).
The Mint has always tried to make as many business strike coins as possible, but I think it's high time that they tried a 'limited' business strike as above. If business strike Dollar coins had been 'limited' (specified maximum production caps) in this manner since 1979, we wouldn't have such an overabundance of them at the Banks and the Feds today (and new Dollar coins would thus be distributed even in a bad recession!).
I think the
Eisenhower dollar would have been much more successful if it had been a 'limited' business strike issue, as I outlined for my $20 coin concept above. (and today the Mint would have the advantage of being able to sell the 'limited' business strikes directly via Direct Ship, and bypassing the Fed.) Even in the 1970's they could have sold the bulk of the 'limited' Ikes directly to the casinos, and the rest directly to collectors via mail order. This could have all been done from one distribution center in Las Vegas!
You could even make a decent argument that if
Morgan silver dollar production had been 'limited', the
Silver Crash of 1893 may have been prevented (or at least reduced in economic impact)!
Let's face it, as long as the $1 note is around, production caps on Dollar coins just make sense!

Apparently, the Mint has never heard the phrase 'too much of a good thing' (since the 1800's

) !