Too much overhead, do not use the network for internal communications. Instead use much more readily available means of communications between different process or what have you. This depends on the system its running on of course...Now you can mimic REST if you like but do not use HTTP or the network for internal stuff. Thats like throwing a whale into a mini toilet.
I disagree. While it is certainly more processing power, a REST-like API provides a clear interface to the application. What happens otherwise, is you have multiple applications using the base system SQL as an API and who, what, where and why another application is calling the base system becomes almost impossible to answer. Limiting the interface to some simple REST-like functionality limits the scope and thus makes future refactoring far far easier.
Beside that, an HTTP request for an internal application does not need all the network overhead associated with a external HTTP request. I believe setting the internal host files to point directly at the server in question would address this issue. As for the performance of a HTTP request in general. Yes it's one more layer of abstraction on top of an already existing SQL interface, however, you could setup lighttp to handle REST requests and keep things light weight and minimal - almost on par with a direct SQL query.