Notifications are generally considered bad because they distract the user from whatever he is doing. Even for things such as emails, new messages from chat etc. people get annoyed pretty fast especially if 1)these come in bulk and 2)have some sound or flashy visual feedback attached to them. Combine these two and you get a very, very pissed off user who will leave your site and never return no matter how valuable information you offer. Do take a note also that your site might not be the only one that uses notifications in the current session which would make the chance of 1) and/or 2) happening skyrocket.
That said notifications are necessary depending on the use case. However notifications don't need be intrusive. If you have a sidebar or similar component in your website you can place your notification there. Example: SMS messages or emails on a smartphone. Of course there is the poorly done notification and the good one. The good one appears in a place which 1)is always there such as the bar where signal strength, time etc. are shown and 2)takes a very small part of the screen. Notifications that cover whatever the user is doing are annoying...very, very annoying. If you place your notification at such a location which is visible to the user all the time and he looks at it (even with just part of his vision but enough to notice a change) you will make sure that the user will see it and at the same time the notification will not be viewed as something intrusive.
UPDATE: The notification type you have posted (should have done it at the very beginning omho to clarify things) has two flaws even though it's a very widely used one - it covers contents of the page and in addition doesn't give any information about the nature of what the user is supposed to allow or block.
Due to it's size the first one might not be such a big issue (although it really annoys me where such a notification covers something that I'm currently reading LOL).
The second issue namely missing explanation is something that I view as a more serious one. If a person is asked a question that he doesn't have enough information about you might think that there is a 50/50 chance of him pressing the "Allow" button. Well, no. At least in my experience you have a much higher chance of him pressing the "Block". This is due to the nature of most users being suspicious (human nature actually). If they don't understand something they often try to avoid it or reject it...or ignore it if no alarm is triggered.
I will talk about the second problem since I view it as the core problem here. If the screenshot you've provided is indeed what you give the user and ask the question "Allow/block notifications" here is a counter example for a better notification (though not perfect) of a very similar nature which we can dissect in order to see what you can improve in your own:
There are two important things here:
I've mentioned that even though better this notification still has a flaw (at least from my point of view) namely the fact that it assumes that the user knows that he can reverse the decision (unblocking for the current session or "till death do us part"). In order to reverse the decision the user has to again click in that tiny area right in front of the address bar:
It doesn't give this information during the initial decision making (namely the allow or block xyz question) and as a new user if I get annoyed by the notifications I will have too google how to reverse my decision. For a user that is already annoyed (but lacks the knowledge how to reverse the setting) having to look on the Internet how to block the notifications is way too much work. Sure, the tiny arrow at the top left corner indicates that something is going on in that area but is this really enough?
In your case you offer a similar choice to the user. In your case your notification lacks any information that might help the user make up his mind. No matter what the notification does it has to inform the user what he is about to do and why the notification has appeared in the first place. The decision making is optional but in your case present too just like the one for blocking the Flash plugin. If you just use the default
https://... would like to use your:
you are not giving your user any information about what kind of notifications he will get. Some web sites for example use a very intrusive way of advertisement through notifications. The missing explanation, the fact that this feature gets abused out there and the missing information how to adjust the settings once a decision has been made lead to mistrust in your user hence the tendency of choosing "Block" instead of "Allow".
A rule of thumb:
Always inform your user whenever you require him to make a decision about something especially if it's about a feature which (according to you) will improve his user experience.
Along with the information what the notification is all about never assume that you know perfectly what the user needs or will use from your feature set. Statements such as
I'm sure, the user wants to know about ... because they applied it. will shoot you in the foot one day. Always allow things to be turned on and off upon user's request. Restricting the freedom of a user even for something seemingly small as turning notifications on and off is a sure path to failure. Make this clear in the information in that Allow/Block notification (again - something missing from the example I've posted above about the Flash plugin!) otherwise your general user will see a one time deal and this is a pretty tough decision to make for anything. A power user will just delete the cookie(s) that you app provides or just know how to open the notification for Block/Allow again and reverse the decision he made and that's that but this isn't exactly a normal way to change a setting, right? :D
PS: My initial post still stands due to the fact that email/SMS notification can easily come in bulk and create a mess. Personally I would try to do some sort of stacking (not familiar with the implementation side of these sort of notifications to be honest). For example: show parts of the message which has arrived first and then add some sort of a counter to indicated that there are more messages after it that require attention.