"Reservation required” means you need a reservation for that specific train to travel. In the examples you mentioned you won't even be able to get near the train without a reservation. The fact that there are empty seats is not important; you still need a reservation. On some trains, like Eurostar, the pass holder seats will sell out before the train is full.

The rail planner app is not always correct about mandatory reservations, but in in your examples it is.

RES can be either mandatory=as above, indeed for anyone, optional (to give you some brain-sussing that there will be  a seat and no need to stand-though often you may have to chase someone away from it on the way-perhaps even another passholder unaware of it all, or not even possible (in about any local/regional train). It does differ a lot between countries how many trains and which types they want you to- this €*, ESpana are the very worst, then comes FR, then IT and the rest is very easy, though some countries do want you to RES all express trains.

It may be possible to forego that by using slower regional trains-like from P to S are 2/day, on the old lines, that take some 6 hrs-like all express trains also did before they opened the hi-speed line which shortened it to just over 2 hrs. NOw you can see what an improvement these hi-speed lines were.

There is a limited number of pass holder seats on the Eurostar and on popular departures and during high season those sell out weeks, and sometimes months in advance.

The best place to see the availability of passholder seats and make reservations on the Eurostar is 

https://www.b-europe.com/EN/Booking/Pass#TravelWish

If you don't get any result, press "later trains" and eventually you will find the next available connection. 

If you have a mobile pass you need to generate a Pass Cover Number in order to make the reservation at b-europe. You do that here in the PCN generator:

https://community.eurail.com/news-and-announcements-39/pass-cover-number-generator-is-live-5653

To clarify why some reservations are mandatory, I believe it is to ensure that those trains do not travel in an overcrowded way and have more passengers than seats. Even on uncrowded trains all passengers require a reservation, the additional cost of which is often included in the standard fares. For pass holders these are always additional to your pass at varying costs.

As in previous posts there are trains where reservations are optional, and on these trains you can indeed just add them to your pass and travel, but with the risk that there are no seats available and you will need to stand.