Okay,
So I realise this was not a run down of Ice therapy all along, My Bad. I will give a speculated guess to physiomitch's question. Ice therapy will not be beneficial to the repair process but it will be beneficial in the inflammatory process and i tell you why.this is a speculated guess but it has good reason.

Before I get back to that, I'm sure we all know that every single treatment technique is claimed to promote healing. the only thing the facilitates healing is nutrients from good fresh blood. Nothing else can do that hence if there is a problem with circulation, respiration or last phase of digestion then most likely healing will be slowed(you see that withmost common systemic diseases,loss in appetite, breathing problems, weight loss,lowed immunity). But then again if fresh blood comes in and the tissues are not able to recieve it because they are dead or the environment is not conducive for them to operate properly(osmosis and diffusion and whatever means of molecular transportation there is) then give all the blood you want to, nothing will happen. hence in infection, the primary reasoning is control watch factors that can increase circulation and if you must, then antibiotics must have been used. if not you would only spread the infection, provide nutrients for foreign organisms rather than host cells etc.

coming back to how ice therapy will not aid repair, in the repair phase a lot has been taken care of, phagocytosis has occurred, new vessels have been proliferated in short the area is now green for vegetation. You bringing ice in starves at that point that is why customary physio practice suggests the use of heat in chronic or long standing cases(and I use the term long standing loosely to mean anything after the sub acute phase). I will give an analogy, burning down a forest ruins the productivity of the land but in a few years fresh organisms will arrive to get the area revitalised and most likely the new organisms will not resemble the old ones that were there before.

So therefore ice will not help repair.

this is where Ice will help the healing process as a whole. By slowing down the rate of inflammation, heat and all them inflammatory agents you are stll able to keep some cells alive. which means your overall transition from acute to subacute to chronic is reduced. if not healing will take a longer time.how much longer?you need a good and well designed study to find that out?probably only effectiveness may be measured because I do not know how ethical it will be to hurt subjects and then see how soon they get better with ice or some other treatment.

but that is all theory, lets imagine we did not give ice. swelling occurs, inflammation is hot vessels are well dilated after being injured, blood comes into the tissues who are stressed already because the place is really heated up(heat causes increase in metabolic rate),the are struggling to take in the new nutrients but they are working at a harder pace, their membranes are ruined, the are recieving noxious substances that threaten to kill them. pressure from swelling is bursting their membranes further,finally everything settles. and it will not settle until the very last stressed severely stressed cell in the vicinity is dead, because that is the only way metabolic rate can decrease. Other cells are safe, but we have left a mass of dead cells which we can not see.

the concept of rest is to provide support to avoid further injury, but rest will also minimise the metabolic stress on that area.Imagine having a strain and still getting the muscles actively working at the rate the would work when they wer not damaged. That is why pain and muscle spasm happens to prevent too much use.

if ice slows local metabolic rate then it promotes healing in that sense. The questions should be, does ice really slow metabolic rate?ice does not aid repair,because it is not needed for repair, infact it is contraindicated in book for repair.

Orthopedic medicine management of musculoskeletal conditions recognises that. so every treatment is graded according to stage in the healing process.
the use of mysofascial release is needed, question is how much and when is it needed?

So rather than asking a question does ice help repair(because it does not), it would make more sense to ask when should I be using ice or why am I using ice in this situation?

Before you can make a direct comparison to nature you need to understand that what nature feeds on is pure. We eat all them burgered slub, cheese and what not and we want to be as free as nature. I think that is funny. A lot of us(myself inclusive) dont have the body that nature designed for us to have. The indigenous tribes you mention eat so many herbs that we in this part of the world can only imagine. They do not have the oily concenterated food that we eat. So how can we compare ourselves to them.

If researches are big businesses alone then how are you able to know what you know?How can one not say for sure that what you have propagated may not have come from dodgy research evidence as well? we wont say that because we know you are capable of dileneating truth from fiction.

instintively, when you touch something very hot or you get burned or an area is hot what do you do?

I think if cells did not die in the early stage of inflammation then ice will be wrong to use but that is not the case.

Other therapies can be considered but there is always a guide to speculate what will work and wont and that is the stages of injury itself.

By the way...I agree with you too much evidence has its side effects.