Obligatory identification while applying for a visa

I can give you some examples (unfortunately none for the Netherlands), but the bottom line is - there are alternate means of identification:

1. In Malaysia, when students submit their passports for visa renewal (a process that can take anywhere from two weeks to three months); they are given a notarized copy of their passport that they use as an ID. It also lets officials know that their status is being renewed and that they are not overstaying.

2. In Kuwait (and other GCC states) the primary means of identification is the national id which is issued to permanent residents and citizens. Passports are rarely asked for or required as a form of an ID. All visitors must carry their passports with them at all times; and a copy of their visas. GCC citizens can use their civil id in lieu of a passport for travel between GCC member states; permanent residents, however, must still use their passports.

3. You can always get a notarized copy of your passport for identification purposes; but unfortunately it is (usually) not valid for travel.

I can't answer this for all countries but for The Netherlands that you specifically mentioned in your example, inside the country a valid drivers license and id card are both also a valid way of identifying yourself. Your case where you are travelling abroad while not having your passport is of course a bit rare, but as you probably know you can use a Dutch id card in Belgium and the rest of the Schengen zone. You are right in saying that your drivers license is not a valid id there though.

That said, I've also never randomly been asked for my id in The Netherlands. As stated in the comments, having a printout and a good explanation wil probably work too in case you are asked to show it.