The problem is when you install 10 plugins, and then 10 others on top of that, and 33 of those plugins you have on your site all push notifications like “You have used this plugin a while, rate us now!” or “Your site is in acute danger of this and that, do this now!” and wether or not those plugins actually let you dismiss the notification in a persistent manner (many don’t, despite the clear rules), then your screen gets messy.
It will tell a lot about the quality and seriousness of the plugin developer and that feedback should go to the plugin developer, not to core.
(On that note, we do not have a feedback way for users to submit to plugin developers here in CP. But that is not a urgent issue, since we also basically have no plugins.)
Plugin review team does their best to spot such issue and would of course not publish something where undismissable notices are found, but we really can’t because often the notices appear after a whole while using the plugin and not just on first install. Neither can any sort of code.
What would be a much wiser move would be to make last parameter of admin_notices | Hook | WordPress Developer Resources actually useful. From the DOC:
* optionally use is-dismissible to add a closing icon to your message via JavaScript. Its behavior, however, applies only on the current screen. It will not prevent a message from re-appearing once the page re-loads, or another page is loaded.
That is basically inviting folks to do it wrong. I am not even sure there is an inbuilt method to actually dismiss notices for good or if all those are actual custom implementations. There are sort of hacks, it seems (like plugins - How to stop showing admin notice after close button has been clicked - WordPress Development Stack Exchange). So … IMO, and if I do not miss anything, the fault for this mess is actually on core API and should if anything get fixed there by providing a proper, dismissible notice hook argument.
So, in that light, maybe we can convert this Petition in an ask to resolve that/Enhance that feature?
Additional info… there seems to be a define('DISABLE_NAG_NOTICES', true);
which users might find useful who want to get rid of whatever notices (but I have never tried it)