And many countries in the Schengen area (not all, though, I don't think) can require anyone to produce valid ID at any time, which for visitors to the Schengen area is almost always going to mean a passport in any case.

Airlines too quite often require photo ID that is acceptable to them at the time of checking in: again, for most people from outside the Schengen area, this will mean a passport.

There are also quite a number of occasions when countries in the Schengen area have re-introduced formal border controls with other Schengen countries, including such things as major man-hunts, major football matches, and contentious international summits.

So best advice is not to cross an internal Schengen border without a valid passport or something similar, even if it is possible to do it...