They do, and so do Permanent TSB. But one crucial difference between AIB and PTSB on the one hand and Bank of Ireland on the other is that Bank of Ireland only offer this discount (and their high-value mortgage discount) to their
new customers. AIB and PTSB offer these discounts to both new and existing customers.
If you are an
existing Bank of Ireland customer, re-fixing with them right now could be a great choice – the rates are very competitive and it is very simple and quick to do.
But if you are looking to switch your mortgage to Bank of Ireland, or you are a first-time buyer or home mover, you run the risk that their rates will be uncompetitive by the time you come to draw down your mortgage. (Bank of Ireland have only increased their rates once so far this year, whereas AIB have increased theirs twice, so we might reasonably expect BOI to increase theirs again quite soon.)
The only sensible approach for a switcher, first-time-buyer or home mover is to apply to several lenders at the same time, get approval in principle from as many of them as possible, and do as many of the subsequent steps as possible before you have to tell your solicitor which lender to try to get full approval (a letter of offer) from.
Even if Bank of Ireland's rates for new customers are still competitive by the time you draw down your mortgage, the risk is that they increase their rates steadily over, say, the next 6 to 9 months to the point where they are again uncompetitive. While you may have succeeded in taking out a BOI mortgage at a good rate, you would be facing the prospect of rolling off onto a bad rate in a few years' time. Then you might want to switch again, which will cost you time and money. And that's
assuming you are even able to switch in a few years' time – your financial situation may have deteriorated before then.
But how can we know that? We can only wait and see how they increase their rates over the next ~9 months (or possibly more).