If there's not much free space on the phone or at iCloud, then there may not be room enough for Photos to delete pictures. Another big effect of not having much free space is major slow-downs in operations.
Do you have iCloud Backup turned on?
Do you have "Optimize Storage" turned on in the phone's Settings>[name]>iCloud>Photos? This allows the phone to have all the same pictures but, by keeping only smaller, screen-sized versions on the phone, it takes up maybe less than 10% of the space on the phone. Or, in another way of saying, iCloud requires at least nine times as much space as is used on the phone.
Here's the most important thing: Why are you using iCloud, and why do you need more space there? The purpose of iCloud Photos is to share pictures with other devices. What other devices are connected to your account?