Why aren't antenna signals inside smartphones stopped by the metal case?
Smartphone cases aren't metal.

Cheap ones are made of plastic (ABS or polycarbonate). The very high end ones which have glass front and back and metal edging will often use the metal edging itself as the antenna. This caused problems on the iPhone 4 when used by left-handers. In that design, the metal bezel was split into carefully sized pieces that were not connected, so that some could serve as antennas of the correct length.

It can be surprisingly difficult to stop a phone working by putting it in a metal box, because the waves are quite short and good at diffracting out of small gaps. What normally happens is it turns up the radio power to its maximum in order to communicate with the base station.