When I started drumming, calfskin heads were still around. The have a beautiful warm sound with few of the high overtones you get from plastic heads. Also, their surface is perfect for brushes.
There are a number of drawbacks to their use, however, even apart from cost, which is quite high.
They do not hold their tuning like plastic heads, and they are affected greatly by humidity, which throws their tuning off, too. When used at higher tensions, such as on snare drums, you really need to detune the drum after use every time, to preserve their life. In the old days you had to mount your own skins on the flesh hoops--a pain. (The Earthtone heads come mounted like plastic heads.) Being a natural animal product, there is a substantial amount of variability from one skin to the next.
Here's a clip of Steve Smith playing a vintage kit with calfskin heads. They are tuned kinda low for the context--a jazz trio, where you'd expect higher tuning--but it will give you a taste of their beautiful sound.
Given that there are several models of heads available these days with the sole purpose of emulating the sound of calfskin heads, without the downsides, there doesn't seem to be much reason to use them anymore.