The notifications you can set up to a normal email address invariably only say that institution X sent you a message, but never specify the topic. That means you have to login to see if it is actually important and actionable or just something you already knew or a confirmation of something you submitted.
Even worse is this common scenario:
* Get notification that X sent something to Berichtenbox
* Login to Berichtenbox (first get mobile phone for required 2FA)
* Message says new information is available in X's web portal
* Login to X's web portal (mijn.somethingsomething.nl)
* Read totally pointless message that could even have been sent in plain email
Compare this to the postal flow:
* Get letter, read it
I think these days you can deactivate Berichtenbox and receive important information via post again, but this was not an option in the first year or so, so even experimenting with it was risky.