Then what is the reason for websites asking me to accept? Some websites also offer me the ability to select/deselect some cookies, but cannot deselect "necessary" cookies. There are websites that do not function until I accept. Some sites explicitly state this, and they do ask me to accept/consent.

Example: https://edigital.sk

On the right, you will see a down-arrow, click on that. You can clearly see the first checkbox on the left being checked and disabled, it is the "necessary" or "essential" cookies to what I am referring. You cannot deselect. On top of that, there is no way to close the popup (?), it is by design. Of course there are ways to circumvent it, but that is besides the point.

There are many other websites like this, but I cannot remember them. :/

I am not seeing anything on your example. But necessary cookies are things without the site can not function (like logging in).

I suppose most of the time the box is there to allow you to consent to additional cookies as well.

There are also a lot of broken implementations out there.

Found another one: https://www.technorms.com

You must click on "Continue with Recommended Cookies", or you cannot use the site (you could use uBlock to block the element, but that is besides the point).