Do users care about notification settings?

Setting the stage:

We have a mobile-app with multiple services from different domains. Each with their own alerts. We are only talking about PUSH NOTIFICATIONS

Problem

We send alerts from those different services. On different times of the day, guided by AI. Now we are wondering if we should allow the user to set those alerts? More precisely; does the user actually care about the settings of his push notifications enough so that he will start looking to adjust it?

Question

Should we allow the user to adjust the settings in our own app? Will they even use those settings or is it enough to rely on the device/app settings?