More exactly, you can't invent algorithms on a spot which took who knows how many years for others to invent. I.e. the question ends up being more if you know about a specific algorithm, which results in "invent it if you don't know about it". It's absolutely silly to test for ability to invent one on the spot, so it's a pretty pointless interview question really.

You can for simple algorithms. It's just really easy for interviewers to overestimate how simple an algorithm is when they have been told the answer.

I hate when it asks for a memorized specific problem, but most of the hard ones I found needs a clever twist of a well-known algorithm, and I still struggle at that too for hard LC.