It could be, but as soon as it is profitable it will attract more people. Plus if no one uses it, the coins wouldn't be worth anything.
The way this could be profitable would be if you mined a coin that not many people use but it becomes popular in the future. But then you might be better off just buying the coins.
RE: Idea: Figure out how to mine a very unpopular currency so you don't have to share the mining task with others?