Getting my Apple Watch actually forced me to go through and get rid of a bunch of useless notifications also from my Phone. I didn't notice them on the phone so much - it was really great to do that.
And I already had a relatively "clean" notifications list, it's easy to get a total barage from all sorts of crappy third party games that want to beg you to play once a day.
The only thing I am longing for now is that I am on-call 24x7 and need to get Phone Calls & Messages.. you can set Do-not-disturb while sleeping to allow phone calls (all or from contacts), but not messages. I'd like to disable all notifications at night except messages or even better yet could set a per-app preference. Main reason is that I have notifications I like for youtube uploads for example, but I don't want them at night time.. which is common because a lot of channels are USA time and I am Australia time.