In my country, we do. For starters, we use apps for authentication and notifications. We can debate whether web push is viable, but most banking apps simply do not rely on it. As for older people, I would rather they use an app than a website because it is far too easy to fall victim to phishing attacks, no matter how much we educate them.
OK continuing to play Devil's advocate: In my country my mom fell to a sophisticated spear phishing attack and whilst on the phone with the scammer and he leveraged her app's login to make it easier and more convenient to attempt to send her money via Zelle.
I wonder if there's really evidence to support that the app's protect you from phishing attacks.
I personally think notifications suck and are spam and not needed, and that we could make something new and better we don't have that today though. What do you use the bank authentication for in your country if you don't mind my asking?