Everything I have read from people I trust, like Pepin and Peterson and so on, fits what chefjohnpaul says here.
If you start the extraction in cold water, the proteins and albumen tend to drift slowly out and stick to the sides and bottom of the pot. If you start hot, they move more rapidly, do not coagulate in large clumps, and are a great deal harder to skim off: what's more some of it will tend to emulsify into the liquid, and removing this by straining (if possible at all) will take with it some of your stock. If you start cold, raise the heat very slowly, and never quite come to a boil, then simmer super-slow and never disturb the ingredients, you will have a stock that is extremely close to clear right from the outset. If you want perfect consomme, you will still have to do a raft, but for most sauce or soup applications simply chilling the stock to freeze any trace fat, skimming, then reducing if and as necessary will be sufficient.
The fact that you eliminate the majority of clarification and the like from the process makes this cold-slow system more efficient: not only does it take less time, but your yields are higher, because every straining or clarification is imperfect and absorbs some of your stock.
I cannot see that ice would help at all, unless you have imperfect control over the heat of your hotpoint, which certainly was the case not so long ago. In that case, perhaps adding a bunch of ice would make it take longer to come to the desired near-boil? If that guess is correct, this trick dates from about two generations back, and does not apply to anyone using modern range equipment.
There is an old trick of pouring room-temperature broth that has not yet been defatted through a strainer containing a lot of ice. The idea is that the fat will freeze solid on the surface of the ice and then not pass through the strainer. But unless you have minimal refrigeration space, I think this just makes things more complicated for minimal result: once it's been refrigerated to very cold, all the fat will be frozen on top anyway, and if you've been skimming assiduously there shouldn't be all that much to begin with.
Somebody mentioned seafood stocks. Here the very slow rise in heat works admirably. If the pot takes an hour or more to come almost to the boil, and the liquid started dead cold, very little albumen and protein is going to be emulsified or bound into the stock, and it strains clear.