Not really, whatever database that's taking orders or serving the catalog can just as easily have thousands of HD addresses dumped into it. Heck, even a day to day wallet that used Nostr for comms could provide those addresses to completely static JS on a site...

Silent payments on the other need a service to actually find the payments, and the user profile shows it won't actually be more private. If we're to assume interactivity with the payment it gets even worse...

Privacy feature = no substance = pointless distraction = worser