You might give your BSN out to a company (healthcare, doctor, etc) but that is used to create the link to your DigiD. From there if you want to login to something like your healthcare company it will then bring up a form where you copy four characters from your DigiD app on your phone. This makes sure the requests match, then you just scan a QR code and type in a pin.
So if you want to login to do something related to your taxes, or healthcare online you have very strong two factor auth.
Additionally banks work similarly for making payments or purchases online. I want to order a pizza for delivery online it redirects me to a payment page on my banks website. I then take out my bank app on my phone, type in a pin, scan a QR, and approve the payment.
What happens when you don't own a phone?
If you're doing online shopping/purchases chances are you have a phone though.
Once set up, you have 3 authentication methods, selectable on login page:
1) password only (low-trust authentication, not all places accept this, certainly not your doctor's office);
2) password + 2nd factor via SMS/text (high-trust);
3) password + 2nd factor via app (high-trust).
I know folks in their 60s who positively would not be able to do any of this with any level of success.
You can make the digital side of things secure while still having accessible method for non-technical people.
This is especially true in this digital age of connectedness and breaches, wherein we're encouraged to use and share the number ourselves in some scenarios, but somehow expect it to not fall victim of a single error or act of malice.
Where is the outrage compared to that of welfare queens, which don't exist in high numbers?
A perennial! problem, hundreds of millions each year. It blows my mind how 80+ years later SSN is still used as identity, far beyond its original purpose. I mean with only one year of those losses US gov. could easily adopt something better.