Good question. I think the main difference is that it is so much easier to visit an annoying website then to download an annoying app. And your GP mentions how a good compromise is to grant this access only to websites you install to your home screen (which I think is a comparable action to downloading an app).
I regularly get spam notifications from major/famous iOS apps. It's always an instant uninstall for me.
IIRC this used to be against Apple App Store rules but I guess they got relaxed for spamming existing customers.
Fastest way to lose me as a customer, TBH, is to disrespect my fiercely-guarded attention span with prompts to spend money while I'm busy being focused on making it.