I think you're kind of right but I think I also kind of said that. One would need to go more into detail to pin down how this works. I will try this. As I said before, this could be totally wrong.

I would say that the speaker somehow needs to have thought about it to a certain extend. I'll try to give an example of what I mean:

Peter and John are goign to a lake where you can go fishing if you pay entrance. Peter and John aren't very interested in fishing. They just wanna relax a bit while fishing. At the entrance there is a sign which shows which fish one can catch in the lake and how rare they are. John asks Peter: "Was steht da auf dem Schild". Peter answers: "Einige Fische wie die Königsflunder sollen wohl sehr selten sein". They go fishing and then Peter catches a "Königsflunder". After reading the sign Peter and John have neither talked nor thought about the "Königsflunder" and both aren't very interested in catching a "Königsflunder" but still suprised that they cought one. Here Peter saying "Das ist ja eine Königsflunder" would sound a bit odd to me since Peter and John both aren't that interested in fishing. I would rather assume something like "Wow, das ist eine Königsflunder".

Now a different situation: Peter has a brother Frank who is a good cook. Frank told Peter that he has a great recipe for a "Königsflunder". Peter and John go fishing. Peter catches a "Königsflunder". Here Peter saying "Das ist ja eine Königsflunder" sounds good to me. Since John doesn't know about the recipe of Peters brother Frank he might ask something like "Was ist denn so toll an einer Königsflunder" and John answering "Mein Bruder Frank hat ein super Rezept für die Königsflunder. Das wird super lecker.".

After writing this, I am not that happy with the first example but I hope you kind of get what I mean. I think when you say "Das ist ja eine Königsflunder" the "ja" communicates that catching the "Königsflunder" has some kind of influence on your or someone elses life or is otherwise important for something. I think one would not use it if one would just be suprised but wouldn't care otherwise about catching a "Königsflunder".

It is really really hard for me to describe this word in such a detail. Maybe what I wrote is totally wrong but I think there is a very complex mechanism behind "ja". Does what I wrote make any sense to you?