In many countries, European countries included, many things cannot be paid with CC. Local transportation tickets for example. Small restaurants, street vendors, countless situations that a CC does not help you a bit.
Yes, Cash Advance is suggested by my BofA CSM too, largely to circumvent the daily limit on ATM withdrawal. In many cases the limit is as low as just $500.
You can use 7-11 ATMs as well as ATMs in the Post Offices. There are also Citis and other major Japanese banks in tourist popular locations that have the international network function.
You should check the exchange rate you are getting - usually you are paying a 5% or more difference buying currency from the bank - just check the Buy / Sell rates. When you "buy" the foreign currency, you essentially "sell" your USD to the bank. Bank does not do this for free, aside from the processing fee. Bank does this to earn the SPREAD between the Buy and Sell rate.
ATM withdrawal OTOH, uses the Multi-Millions Interbanks settlement rates which are much much more tight spread, usually less than 0.25%.
ATM cards are much safer than bring cold hard cash. You do not bear the risk because any fraudulent usages, if there is any, as long as you report it in time (within 60 days of the statement where such fraudulent charges occurred), you are not responsible.
Yes, Schwab is Great. They also reimburse the ATM fees which in many Asian airports ATMs charge fees. I have seen that in BKK and ICN recently.
Citi, Chase and a few big Japanese banks all have international network ATMs but as you said, outside main tourist areas you could not find any. BUT 7-11 ATMs all work as Citi partners with them from years ago to offer such service.