I study real mobile traffic in great detail in my day job.
I see a several problems with this.
Half of all mobile traffic is video (by volume), and it's mostly YouTube which is encrypted.
There is little point to stream video much faster than you consume it, plus a bit of buffering, as they might abandon it.
Typically only have a few hundred users in a cell the chances of them asking for the same content are slim - OK say BBC home page, or all the news, but so what? it takes only a fraction of a second on the backhaul. E.g. everyones Facebook page is different.
There is already HARQ (Hybrid ARQ) for caching the stuff actually being downloading/looking at the base station.
Latency, the radio network latency in LTE is insignificant compared to all the other contributors.
The top 10% users are responsible for >50% of all traffic (usually bit torrenters or something) and in some networks enjoy grandfathered rights (unlimited means unlimited!)... So chances are most of the data volume you see on a site is a handful of people.
Typically 20% of sites carry 80% of traffic, it isn't evenly spread about (this seems to be a surprise to some people in the industry).
The cost of backhaul is indeed significant but I think (I have no simulation to back this up) based on real life user activity, the type or traffic, the levels of encryption, the low numbers and low likelihood of users in same cell asking for same content makes bae station caching the whole internet impractical.
Its Jevon's Paradox for bandwidth - make it faster/cheaper people will use and waste more of it...
Does anyone know if ISPs (still) cache the some traffic into their own networks?