You can't go on the direct trains between Germany and Denmark without a reservation, but there are reservation free option with several changes on the route from Hamburg to Copenhagen. 

Some travellers have reported  there are ticket checks and people without reservations are taken off the train. The problem is the direct trains but there are other change options. Use the app with the no reservation option. Then go to the DB site and DSB sites to check. Going via Niebull might work but you’ll need to reserve on the Esbjerg to Kobenhavn train. Alternatively travel to Fredericia and change there. You’ll need reservations on both the trains. DSB and DB allow seat only reservations and they are sent by email.

Assuming the train requires a mandatory reservation for Interrail users, I would expect the conductor to deem your pass invalid for that journey and charge you the full fare or eject you at the next station.

I assume you have exhausted all the reservation services available to you (eg DB, OBB, rail europe and even interrails own.

I have had a go and first look shows the same but I think it may be a glitch in how the trip is constructed.

I have just tried the Interrail reservation tool for the leg from Ham to Cop on a couple of days in Aug/Sep and it shows availability on direct trains and several combinations where reservations are not needed (with changes). I obviously didn’t put them in my cart but maybe you need to split the legs for your specific dates. The system of planning a whole journey in one often misses slower combinations for individual legs.

Can go on the day=not in the night nearly ev 1 or 2 hrs-RE to Flensburg (some start from the other HH stop=Altona)-DSB then change Kolling or Frederica-other as above suggests IC-trains IN DK do NOT have mandatory RES. Also: maybe yiu-but as seems normal for every newbee no exact details were given- the RES for the direct trains can ONLY be done via dsb.dk- cost is 30 DKK and RES comes by mail. The route via Niebüll-Dageb:üll is far more time eating.

You know-about every day we see here scores of Svenskarna, following the urgent advice of a certain Gretha to go by toget och inte fly-a few weeks ago it was them going sóderut, and ny kommer tilbage hemmet-tell her how it works in practice if you follow the conseil.

BUT there is hope for next yr-as DSB knows the prib-and is also very eco-unfriendly in sending old short dieselsets over the 500+ KM : they have ordered old trains to make new and will next yr offer many more toget with mycker mere siddeplasser.