Paol
 Do most salt mixes replenish potassium, iodine and strontium?
Yes they do.  The issue is do you need to sup them. IMHO no. 
Sr++
Is only  adsorbed by coral because it is there. Corals also have Uranium in their  skeleton. So, should we start to dose that too ? It is pretty much just a sales  gimmick as there is zero evidence that they need it. Sr++ is a substitute ion.  Meaning, if it is there it fits into the Aragonite crystal lattice real nice,  just like Calcium. What about Magnesium ? Hope it does not fit into the  Aragonite crystal lattice. However, it does fit into the Calcite crystal lattice  real nice and Strontium does not fit into the Calcite crystal lattice. Why ? It  has to do with the ionic radius of the ion and the "cell" structure of Calcite  and Aragonite. For Calcite, Sr++ is to big and for Aragonite Mg++ is to small.  That tells you what ?  That Ca++ is right in the middle on ionic  radius.
IR Mg++ = 1.64 A
IR Ca++ = 1.97 A 
IR Sr++ = 2.15  A
Iodine
First, it is not Iodine, heaven forbid but mostly  Iodide, with a tad of Iodate. Is it needed ? Yes. Do you really need to sup it ?  No.  Why ? Most tanks seem to have actually to much of it, above NSW levels.   And most do not sup it at all and many have spectacular reef tanks without it.  Last, almost all marine life really do not adsorb it but get it from their  "food".
One theory throw out there, haphazardly, is shrimp need it.  Shrimp get it from their food. You over dose with "Iodine" or get it to high you  will drive them into a continuous cycle of Ecdysis, which will kill them and the  same for other Crustaceans.
Zenia: My theory is you dump in "Iodine" to  get them to pulsate more is they are pulsating as you pissed them off and they  are trying to get rid of it. Pulsating vs non-pulsating is mostly a water flow  issue. Ask yourself the question, why do some pulsate and others do not  ?
Potassium, K+
Mostly a Zeovit kick, because of the way they run  those systems. And most non-Zeo system are near NSW. It is due to a K+  deficiency, where you may see a washed-out appearance in Acro's, especially a  loss of blue coloration. IMHO if one does normal WC it should not be  need.
I have no issue if one wants to keep any of these at NSW  levels or any ion.  If you want to do so then test for it. If I had to choose  one it would be K+. However, testing procedures for this ion are not easy and  can be way off. And it would be nice to know what the iodide level is at. For  Sr++ it is a waste of money.