The solution to reuse a number is bat shit crazy. Perhaps they can use expired cards (and not cancelled).
In the long run the sensible solution (just like IP addresses) is to move from a "IPv4" system to a "IPv6" that will largely multiply the available numbers per country/bank/entity and will solve the problems, for the next many decades.
For example, Mastercards start in the range 51 to 55. That leaves 4 digits of the 6 digit BIN to allocate to MC issuers. So that's a total of 50K issuers of MC world wide, then each of those issuers can have 1 billion cards.
So each issuer of a MC in Japan can issue a card to each member of the population and only use an eighth of their allocated range.
The problem isn't the individual card account ID, from the article, it sounds like Japan has been allocating too many BINs.
Assuming your calculations are correct, this means an issuer can only emit 8 cards in average to the total population.
Cards have an expiration, people lose them, break them, they change and come back to banks. For the main issuers it’s not ridiculous to have to issue 20 or 30 cards per account to a user in their lifetime.
Then people have multiple accounts (e.g. my mortgage was on a separate join account).
There’s just enough normal circumstances to run out of numbers, not even considering freak cases.
You understand that every possible prefix / range has a billion numbers minimum? That japans population is only 125 million?
And actually - you can near randomly assign numbers if you wanted, looking up card issuer is not difficult. Can basically issue card numbers in blocks of 100 if you wanted to reduce lookup tables a bit. This is already happening and available actually. Visa and other (apple) offer tokenization services to randomize your card number. Every phone number uses this type of system to enable number portability as well (you can take your phone number from t-mobile to sprint).
With 16 digits (1,234,567,890,123,456) you have 999 trillion numbers you can assign. As my original comment pointed out, the idea that we are running out of credit card numbers is absolutely ridiculous.