AIB and BoI have been around in some shape or form since the 19th century.
That makes them older than 99.99% of other Irish enterprises and indeed the institutions of the state that (part)-owns them.
They will remain profitable because they are the incumbents in a small market with huge barriers to entry.
I’ve been a customer since AIB gave me £20 a month for three months as a student for keeping my balance above zero.
The only thing that AIB have done with technology is online banking, which actually has a very good user interface and functionality by retail standards.
Their core business of hoarding the cash of the frugal elderly and lending to reckless youth is unchanged. As long as people need savings and loans then AIB will be round and making a profit doing it.