According to a report from XDA Developers, it appears that Google is working on introducing some changes to Chrome on both Android and desktop that will make these prompts less intrusive. For example, on Chrome for Android, the new flag reads, “Enables quieter permission prompts for notification permission requests. When a site wishes to show notifications, the usual modal dialog is replaced with a quieter version.”
However, for Chrome for desktop, it seems that Google could be looking to block these prompts entirely. The flag reads, “Notifications are currently blocked for all sites except for sites you individually allow.” It also seems that Chrome could eventually learn about what you prefer, where it seems that if you keep blocking notification requests a few times, it will block all of them automatically based on your past habits. However, note that these changes aren’t actually live yet so there is no guarantee that it will become an actual feature.