Note: I will be talking about removal, or failure to introduce, of large-ish denominations.
Lack, or rapid reissue, of large-ish denominations tends to happen in countries with bad economy and low confidency in local currency already.
Known examples are India (reissuing 500 and 2000, discussed removal of 2000), Argentina (the largest denomination was 100 {~10 USD} during the existence of 'Dolar Blue' and falling rate of the currency), Soviet Union (secret denomination of 1961 and bank note reissue of 1991), North Korea (2009 reissue), Zimbabwe (google zimbabwe wheelbarrow of dollar
).
Strong economies usually see no problem having large-ish denominations of their currency in use even as electronic payments are also very well developed and grey economy size is relatively small. A curious example is EU which sort-of deprecated 500 EUR note following economy instability period.
I will theorise by that example that it leads to short-term fiscal normalization / rent-seeking on the side of country government at cost of citizens' misery. Why is it only short-term is because it tends to encourage foreign currency holding and will often go alongside (hyper)inflation.
In many cases banking system which goes alongside is non-existent (Zimbabwe, late Soviet Union), untrustworthy or predatory (such as Argentina with its exchange ratio fakery), so we can't talk about honest encouragement of using non-cash money.