I can see memory challenged, but not privacy conscious.
The big problem from my perspective is in the user experience. On my first visit to a site, they ask me if I want notifications. It's my first visit, I know nothing about the site. Why would I say yes? Later, if I had changed my mind, I might want to, although in most cases, I'd rather just use an RSS feed and get updates when it's convenient for me rather than for them. I have yet to encounter the scenario where website notifications are better than old-school RSS.
On the privacy front? I don't see how this helps in any way with privacy. It seems like it would be more likely to be a privacy nightmare than a privacy boon.
> Can you appreciate how a memory challenged/privacy conscious person might find it helpful to opt in to web push notifications?
By relying on Chrome, the least privacy conscious web browser in existence? Not really.
Just make an app. All of the benefits, fewer privacy compromises. But, it requires more work on the developer's end, so I also understand why they might not want to. Just stop trying to paint their decisions as being privacy conscious.