Just for advice:
We plan to travel from Nuremberg to Brussels 26 August 1st class. Although reservations are not compulsory I thought I would check availability on DBbahn. I was amazed that the journey was showing as high demand so decided to see how many seats available. The ICE from Nuremberg was already about 70% booked and the ICE from Frankfurt was about 80% booked and few pairs of seats available.
11.80 euros later we have reserved seats on both.
Alternative later trains showed low demand so I guess it is only peak trains that may be full, but always worth checking.