Is it a cliche?
What is the alternative if I want to describe one's feeling when he/she is doing research in some field?
This means "the more I research and attempt to find the answer to my question, the more questions I have." If a "cliche" means not to use it, I would say it is not a cliche (you can use the expression). I also use "ignorance is bliss" regularly, so maybe I am not the right person to answer that.
In an essay, I would not be afraid to use it to show that you have fully researched and thought about your thesis. However, I would be sure to find a conclusion to the thesis and have well-reasoned analysis rather than using the expression to excuse questions that are raised that are not ultimately answered. If your analysis raises questions that are outside of your thesis (are not relevant), why highlight those? I think that just confuses things and detracts from your conclusion. That is a writing style suggestion and not an English language issue.