Plastic deserves some attention since I believe there are some very common misconceptions. Let me first get this off my chest, and then I'll try an elaborate:
There are very low quality plastic instruments! There are also very high quality plastic instruments!
Here's some food for thought:
Many people associate plastic with cheapness of quality, especially in musical instruments. One reason perhaps is because there are many "toy instruments" out there which are usually made out of plastic.
There is an absolutely huge range of different plastics and an even bigger range of uses. Try not to make generalizations about plastic musical instruments.
Some plastics are very high-tech materials and have very specialized characteristics. For example, polycarbonate is very tough and is used for safety glasses and bullet proof glass. Some plastics are cheap and some are very expensive.
Some economic considerations...
The main reason you would make something (including the ocarina) in plastic is because you want to make a bunch of them. The basic idea is that you spend a pile of money to have molds/tooling made, and then you can make as many parts (instruments) as you want at a low cost per part/instrument. You would probably spend anywhere from $5,000 to $80,000 to make molds for something like an ocarina.
There is a large difference in quality between low end and high end molds. In other words, you could have some very high quality plastic ocarinas made from high quality molds. If you want fine musical instruments (as opposed to toys or trinkets), you would need high quality molds. If you just wanted toys, there wouldn't be much point in making high end molds.
You have to make and sell a whole bunch of ocarinas to recover the costs of the investment in the molds/tooling.