Yes, Speaking from experience , It's one of those things that one eventually forgets to do without any consequences and then something happens making you wish you had sorted it out at the time.
If for example an ATM machine swallows your card you'll need to visit a branch to sort a replacement , they will want to see your passport and if the number doesn't match the one on their system they will want to see the old passport and the new one when they update their records. The sooner you do it the less likely you are to have discarded or disposed of your old passport
When it happened to me I had changed passport twice since opening the account and my old passports were back in the UK. The people in the bank were very reluctant to issue a new card, Fortunately my brother in law had needed a lift to collect his car which was in for repair, and had accompanied me into town that day , even luckier he's a cop and he had his uniform on, Him vouching for me being who I said I was made all the difference.