Several beta users have asked for an album or gallery view that shows photos and videos taken on the current day, or the current week, but from previous years.
(Google Photos does notifications when these are available: I’m normally opposed to notifications, but if they’re coming from your own library, and they’re opt-in, not opt-out, it seems like this wouldn’t be noxious)
I can’t wait for you to mark some items as done so I can get some votes back and vote for this one!
Are users specifically asking for a notification? I’d be perfectly happy with an album that I can click into whenever I want that shows “On This Day (or week)” for previous years. With that said, I’m not opposed to a notification as long as it can be disabled!
The most important user I’ve got: my wife 
Can’t argue with that!!
Relevant discussion:
Are there plans for mobile phone apps, Android and iOS? I’m not sure how else you’d do notifications. Maybe you could do opt-in daily emails or something? I agree this is a very cool feature of Google Photos and Microsoft OneDrive, and dramatically increases my appreciation for my old photos.
Desktop browsers and mobile browsers on Android have supported push notifications for half a decade now, and iOS is supposed to deliver support for notifications in 15.4 (oh, wait, 15.4 shipped and it didn’t make it, so perhaps the next release?)
Point is: native web-based notifications are almost available everywhere, and soon will be.
Related: URL for random image - #12 by devon
Interestingly (at least to me): Google Photos doesn’t have a specific UX for going to “this day” or “this week”: there’s now a carousel at the top of the Photos view, and that sometimes has a “1 year ago” or “2 years ago” album.
I suspect most people view this feature via the app notification, rather than navigating to it on demand.
I really like the Plex way of doing it. There’s a screenshot in this similar feature request over at Photoprism:
I stumbled across this thread because this is exactly the feature I’d love to see. A “Show me all assets on date X for any year”,or “Show me all assets taken during week Y for any year”.
I’m not fussed about notifications, but just having it as a pre-canned query on the search page would be good enough for me. Of course, combining with location or favourite or other metadata would be an added bonus.
Maybe it’s already there (I’m on 1.1.0) 
Wow, just moved all my photos from my OneDrive storage to my NAS, and now really missing the “On this day…” notifications+emails I used to be getting.
First priority feature update after next stable release is support for multiple users I know. Hope this one isn’t long after 