RugbyRebels

Essentially, applying ice starts up a hunting reaction, as the blood vessels in the area respond to the change in temperature.
Initially this starts with vasoconstriction (narrowing of the vessels) as the body panics a bit that it's going to lose core temperature; then it over-reacts the other way into vasodilation (expansion of the vessels); and hunts around for a bit until it finds a new level it's happy with and settles down.
The time frames of this hunting reaction depend on a LOT of different factors (temperature of the ice pack, size of ice pack, temperature of the tissue, size of the tissue [eg. finger versus torso], quantity of subcutaneous fat, vascular & neurological health etc etc).
Another effect of cryotherapy is to slow nerve conduction => less pain (impaired mental function and repairing nerves are already relative contraindications to cryotherapy [amongst many others] - I'll be really interested in how this study squares that circle - but I'll also admit that neurology/neurophysiology is ridiculously complex, and I struggled with them 25 years ago).

Vasoconstriction has an anti-inflammatory effect (starving the tissue of blood, oxygen, and the various building blocks it wants to heal the injury) - it's what you want on the sports pitch, where you want to minimise bleeding / bruising, and deal with the injury properly later (and why pitch-side, you should never use the ice for more than a couple of minutes).
Vasodilation has a pro-inflammatory effect (flushing the tissue with blood, oxygen, and the various building blocks it wants to heal the injury) - this is where the advice used to be to use the ice pack for 10-15 minutes on, and leave it off for 60-90 minutes before re-applying.

These effects have been seen in a really small way, at the level of inflammatory markers.

Inflammation is the first stage of tissue healing, so we really don't want anti-inflammatories unless it's actually indicated by an excessive inflammatory reaction (as opposed to as standard, just because).

We also know that patients are frankly terrible at taking advice (especially if it's given by people who are terrible at giving advice, don't explain the advice, and often, don't understand the rationale behind the advice); and therapists are currently running scared of inflammation - "first do no harm".

In my opinion:
A] Yes, patients are idiots, but so are therapists. Explain the rationale, and treat the patient like a grown-arse adult (or their parent/guardian as a grown-arse adult), then even if they forget the time-frames, they've a far better chance of using the stuff appropriately.
B] Appropriate use of ice is appropriate, inappropriate use of ice is inappropriate.
Whilst we have evidence of cryotherapy effecting inflammatory markers; as far as I've seen, we've not seen that that effect is actually relevant to patient healing times.
C] I've been doing this shit long enough to see various other babies being thrown out with the bathwater based on "common sense when you think about it" rather than actual evidence (or simply poor evidence), only to be rediscovered as useful a decade or two later.

My practice:
I still recommend ice; but way less often than I used to (doing my accounts - I sold 3 ice packs last year; 18 years ago when I opened my own practice, I got through a box of 50, and into a second box). When I do, I explain the what and why to the patient, along with the potential adverse effects, and follow up by email. The ice packs I sell have the time frames written on them.