With SEPA I've been required to use the IBAN even for transfers within Germany. Which isn't all that different, as you only need to remember the two check digits and the order in which the old numbers appear within the IBAN. The UK and other countries that continue to use their own currency are a bit special regarding domestic payments, though:

SEPA does not cover payments in other currencies than the euro. This means that domestic payments in SEPA countries not using euro will continue to use local schemes, but cross border payments will use SEPA and euro against eurozone countries.

But you wouldn't see such a distinction in countries that use the Euro.

You can use IBAN domestically in the SEPA area for EUR account numbers. The banks usually allow the use of bank account numbers too and they then translate them to IBAN, so you don't have to. What's more, account numbers in some countries themselves contain check digits.

A Norwegian bank account number has it, so I guess it depends on the country