So it basically comes down to, we do the typical recommended 10% weekly water changes because that's what everyone's been doing for a long time.
Unless you're doing ~50% weekly water changes each time...
The trace elements idea is bunk.
The pollution diluting idea is bunk.
So why do we do water changes again? And how is it possible there are some very impressive SPS reefs in this forum that don't do water changes or do them extremely rarely.
This is simply untrue, and with a little bit of math, we can calculate where you will reach steady state at any given consumption level. In fact, I just had the same argument earlier this week, so I'll just re-post from that thread:
If we start with the assumption that our synthetic sea salts contain the appropriate elemental composition for our livestock (which I think is entirely reasonable, and if not you should pick a different salt ), and we accept that there are many things required by our livestock and that could potentially harm our livestock that we can't reliably measure for (trace elements, compounds form coral alleopathy, etc.), then a few things become plainly evident. 1) We cannot "prove" they are depleted without sophisticated laboratory equipment that can measure very small quantities of each compound reliably, 2) Even if we did that we cannot monitor all of these compounds to ensure they are within their required ranges cost effectively (i.e. we cannot reliably test for and dose them by themselves) and 3) No matter how their concentration varies while in our tank, by removing a proportion of the water and adding new synthetic sea water, we by definition move them closer to their target ranges.
Mathematical explanation. English translation below. Feel free to skip the math if you trust me or hate algebra.
With regard to your second question, lets do some math. Lets take a tank of some volume "V" and change 10% of the volume at some time interval and track what happens to our mystery trace element, call it element X.
Element X is kept at a constant level over time when the amount brought into the system by a water change is equivalent to the amount consumed between water changes plus the amount removed by the water change itself. Obviously, if the element is being consumed without replacement, it will have to achieve steady state at some concentration lower than the level found in your freshly mixed ASW (barring a 100% water change of course.) Lets say element X has a concentration "Cb" in your freshly mixed water (in the bucket) and "Cs" for the water in your system. Between water changes, your tank uses up some fraction "f" of that element in your system. We can then write the equations:
0.1*V*Cb = mass of element X added by a water change
f*Cs*V + (Cs*V - f*Cs*V)0.1 = the mass of element X consumed by the tank plus the mass of element X removed during the water change
By the law of conservation of mass and steady state assumption we get
0.1*V*Cb = f*Cs*V + (Cs * V - f*Cs*V)0.1
When solved, this leaves us with:
Cb = Cs * (9f + 1)
For explaination's sake, lets say the level in your tank is 50% of the level in your freshly mixed seawater (idk, just picking a number there).
We can then add the equation
Cs = 0.5 * Cb
Which when substituted into the above equation, leaves us with
f = 0.11
English resuming. Thanks for your cooperation
Which means a 10% water change will keep the level present in the tank constant when the amount consumed by the tank between water changes is about 11% of that found in your tank (assuming the level in your tank is at 50% of that in your bucket). Where that "steady state" happens is determined by the concentration in your salt an consumption, which is usually related to the concentration in your tank, so it gets more complicated than what I've shown based on a number of variables, but the concept is always true. I guess my point is, it's not nothing, mathematically we can see water changes have a non-trivial effect.
Finally, with regard to the statements regarding SPS tanks without water changes for years. Even if it is true, citing the exception to a rule when dealing with populations doesn't mean the rule is wrong, it just means you're citing the exception. My grandfather ate bacon and eggs every day of his life and lived to be 80 years old, completely able to move on his own and completely mentally in-tact -- that doesn't mean that bacon isn't bad for you.
Keep in mind, that article was written by two people who were working at the time for a company that manufactures artificial salt mix 
