When I moved from the USA to New Zealand in the early 90s I was surprised at how much easier the banking was. Sure it's a much smaller country with only about 25 banks (about six banks have most of the accounts). The key here is that every account number has the same format and is unique across the country, and the banks co-operate to make transfers easy. Paper checks are so rare you can shop for weeks and never see anybody pull out a checkbook. A debit card system (EFTPOS) was live in the 90s and all of the big consumer banks supported it; soon most shops supported it too. If you are using the web, paying somebody in a different bank is as easy as if they were at your bank. If you pay somebody at the same bank as you the money transfer is nearly instant; if they are at a different bank it may take 1-2 days.
It's not fair to compare a country of 318 million with a country of 4.5 million, but a little co-operation between the big players might be a good start. New Zealand's banking co-ordination was the result of an industry consortium, not a government agency.