Right, I'm aware of having an effective Faraday cage around one's phone if one want's to shield it against the ingress and egress of RF energy. Unfortunately, in some areas (and that includes around where I live) that can be problematic. Unless the shield is very effective it can leak sufficient RF to still function. Leaky shields that I didn't expect to leak included containers like used sweets tins where the tin-plated top completely overlaps the (tin-plated) base. It seems that with a good line-of-sight to the tower and using frequencies upward of 800MHz that any slight oxidation of the tin allows RF to leak inside the container.

I'm not sure why these seemingly nearly perfect Faraday containers can be that leaky but they can be—often to the extent that the phone is able to 'dial home' to the tower. Also keep in mind that tin oxides can be both conductive and semi-conducting, which means that intermodulation is likely to occur around the edges of the lid (remember, tin oxide is unusual in that it is both conductive and essentially transparent which counts for why it's used as electrodes in vidicon and image orthicon camera tubes). Perhaps the problem was that if any oxide was present then it was unlikely to be visible (but solving that matter is for another time).

Anyway, I didn't research the problem in depth—as it was more a nuisance than a curiosity. A short while ago I spent a considerable amount of time rooting various Android phones and I didn't want them to call home before I'd finished (as I couldn't get a completely clean install) and it turned out that the leakage problem was significant—and a damn nuisance. To solve the problem with several of the phones, I resorted to opening them up and shorting out the IC pins that lead to the antenna.

As you mentioned, there's another problem with carrying a switched-on phone around in a Faraday cage and that's gaining physical access to the phone before it connects to the cell tower. For example, you may want to switch it to Airplane mode before any connection with the cell tower is established but essentially it's impractical to attempt it unless you are also completely within another much larger Faraday cage.

The fact that these days most phones have non-removable batteries is a first-class damn nuisance to say the least. I have some cheapie phones I use for testing and they have removable batteries and that's invaluable but it's not so with the high performance ones.

In this regard, the best phones I've ever owned were the old Nokia ones that used the three different sizes of detachable batteries (small, medium and large). One could remove the battery in an instant by just pushing the button on the back of the battery nudging slightly until its contacts parted with the phone. This instant detach feature was especially useful if say you were in a meeting and had forgotten to silence your phone—the instant it rang you'd reach into your pocket and voilà the battery and phone had parted company.

What's so annoying these days is that manufactures don't consider such features as important (or more likely they consider them undesirable as during a disconnection you'd likely lose some of that spy data that Google so eagerly collects (now we can't have that happen can we?).