That was a great post. I think you phrased your question in a way that maybe will help clear some things up.
First of all, I need to tell you that I do not know enough about symmetry to comment on its relationship to Dick's work. I didn't understand Yanniru's earlier challenge that Dick had assumed symmetry, and I didn't understand Dick's rebuttal to that claim. I also checked into the Emmy Noether site that Alex told us about and I only glimpsed the concepts but not the details. So any time I mention symmetry in this answer, it is only a guess on my part. Now let's look closely at what you wrote.
***If symmetries are a necessary constraint on physics, and symmetries create most of physics (e.g., the achievements of Emmy Noether), therefore, it is already known that the laws of physics are under special constraints - nothing new is obtained. ***
I think Emmy Noether has shown that the laws of physics can be derived from symmetries (or something like that). The question then, is, Are symmetries a necessary constraint on physics? And if so, how could we know they are?
As I see it, there are a couple different ways we might know, or at least strongly suspect, that symmetries are a necessary constraint on physics: 1) by using the methods of traditional science, and 2) by using Dick's method. These are quite different methods I will talk about later.
But, for now, let's assume that somehow (either using 1) or 2) or some other method) we have come to know that symmetries are a necessary constraint on physics. With this assumption we have satisfied the premiss in your initial statement and we can infer "that the laws of physics are under special constraints".
Now let's look at those two ways of coming to know that the premiss is true. I.e. that symmetries are a necessary constraint on physics.
1) Observe phenomena; notice symmetries; suspect the premiss is true; develop predictive theory; run experiments to corroborate and support theory.
That is the method of science, and it has given us remarkably useful results. But...logically...no matter how many experiments you run to verify a theory, you never reach certainty about your premisses (I think that's the English spelling). The best you can do is strongly suspect it is true. You can't really say you know it is true.
2) Assume parts of the universe are communicable (i.e. describable); notice that descriptions and communications are sets of numbers; derive constraints applying to arbitrary sets of numbers; notice that those constraints are the same as those suspected as a result of 1).
That is Dick's method.
***So, I don't understand the big deal. It is just telling us something that we already know.***
***nothing new is obtained. ***
Let me address this by making up, and then telling you a parable (I'll base it on a true story that happened to me):
One day your car starts having some weird intermittent electrical problems. It is an old car and you do not have a wiring diagram. You get your screwdriver and your meter out and start searching. You take things apart, test things, try things, scrape your knuckles, and get frustrated. You resort to tracing wires and laboriously begin to draw a diagram of the circuits so you can understand how it is supposed to work and then maybe isolate where the failure is. Oh, if only you had a wiring diagram!
Finally, after much agony, trial and error, and more bruised knuckles, you find the source of the problem and fix it. Just at that moment, your brother-in-law comes by and hands you a wiring diagram for your car. You look up at him and say, "nothing new is obtained".
For that particular problem, I guess nothing new is obtained. But, if you're interested, you could check your heuristic wiring diagram against the "true" wiring diagram. You could also thank your brother-in-law for the "true" diagram and use it later for other unforeseen troubles with your electrical system.
To sum it up, I think that what Dick offers is a "true" description of the constraints on a communicable universe rather than the really-really good guess offered by science. He offers a basis on which new theory might be inferred using the same techniques he used to derive the then-known laws of physics and the same techniques used by physicists to derive the same thing once they suspected that symmetries constrained physics.
***It seems to me like Dick has 'discovered' that symmetries result in the laws of physics. What is incorrect in this assumption? ***
I think it is incorrect because that is not what he discovered. Instead, what he discovered is that communicability (or describability or explainability) results in the laws of physics. I think that is much more fundamental. I think the symmetries just peek out and smile at you along the way.