What are the disadvantages of using FPGA dev kits as the 'final product'?
The biggest one is that it might not be available tomorrow. 

In some cases, the manufacturers intend that the development board may be used in low volume production and pledge to maintain production over some period of time. They may also make available schematics and gerbers that allow you to produce the boards yourself. 

Producing a compatible board over a long period of time is a significant commitment- like making a product. They have to deal with components that go obsolete, document changes and so on. 

Other disadvantages center around the fact it wasn't designed just for your application so it might be too big, too power hungry, lacking in features etc. 

OTOH, the relatively high production can have advantages. The cost of a development board for an aerospace client of mine was less than the cost to just populate an equivalent bare board (that's before buying the parts or testing).