You need seat reservations for most trains per my understanding. They're cheap and flexible so you're mostly right, but it's a little more involved than "get on whenever you want" unfortunately

It very much depends on the operator; Eurostar and SNCF requires very expensive seat reservations for all TGV services, but hardly any services in the German-speaking countries do so. More important than the price though is the availability - only a small proportion of seats are open to Interrailers on the French trains, so if they sell out you could find yourself unable to board a train that is still half-empty!

The situation in eastern Europe is more variable, but the reservations aren't generally as prohibitive as in France.

Ah, I thought ICE also required reservations but that's only the case if the train is otherwise booked out (source https://travel.stackexchange.com/questions/72538/what-if-i-u...). For me, trains like TGV, ICE, and perhaps Nightjet make up the bulk of the distance to most places I go, so for me the reservations were pretty much required no matter where you go; apparently not really for ICE then!