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.
Are you sure that there aren't unpopular coins that are very profitable when mining just because you don't have any one else competing with you at mining them?
In theory maybe. But the thing that makes currencies valuable is having people use them, or in other words, popularity. So if no one is mining or using a currency, it will have no value.
For example, if you built a product that no one else builds you won't be able to sell it unless other people want it. So unless you find something that people want they just don't know it yet, you would be wasting your time.
So if you find a currency that is unpopular now but you think that in the future it will be, you could mine it (or buy it) and hold it until it gets more valuable.
There are a few websites that calculate how profitable it is to mine different cryptocurrencies. If there was a currency that was extra profitable, it would show up at the top of these lists and people would start mining them until it wasn't profitable anymore.
Here is an example website.
https://www.coinwarz.com/cryptocurrency
Hope this helps, sorry if I'm confusing. :)