Chess 960 is a popular chess variant that can be played on many platforms. All rules are standard, except the starting position is randomly generated. Some of these 960 positions give more than usual advantage to white. In some of these 960 starting positions, the king is not really safe even after castling.
One big de-merit of chess 960 is the complicated castling rules. A case is made for chess without castling in this answer by Remellion (also, see other answers for the same question).
So, why not kill two birds in one stone?
What are the Pros and Cons of introducing chess 960 without castling as a new chess variant?
It may or may not take off. But, there are so many chess variants now. So, I don't see any demerit (see this answer of Jeorje for related comments). I have seen this suggestion in forums (example). But, this variant is never made nor considered seriously to my knowledge (e.g. currently, we cannot make this with make custom variant option of chess.com). To be fair, one could play this in existing chess 960 platforms by inserting some initial moves that manually moves all 4 rooks or 2 kings and then get back to the initial position (see the 1st position is this answer for an example).
Why is not chess 960 without castling considered seriously?