The problem of maximizing your self-interest in a market is general enough that finding a solution to it can require solving an NP-hard problem. This is actually true, real financial problems are NP-hard.
The market does not optimize for resource distribution, it optimizes for profit. It is tyrannical in that it removes your agency, as a member of the market you have no other choice but to optimize for profit in many important situations.
This is already dysfunctional enough to completely destroy a society, so we have to implement fictions like IP and regulations to tame the beast.
As far as central planning goes it's certainly possible to plan an economy while allowing people to choose their jobs and start small companies.
A sufficiently advanced AI would inevitably be more efficient, simply releasing all IP restrictions, all binning that is not necessary, ending all unproductive landlordism, and the compound growth from the lack of crises would do it.
Now you could be opposed to it from an ideological point of view, but no matter what you're misstating Hayek's point, as he contends that it is not, actually, possible to perform the economic calculation outside of markets, due to computing brain magic of humans only when they act that way.
Also, the mere principle that a market can run the economic calculations more efficiently than another computer is a violation of the Church-Turing hypothesis. There is no machine that we know of that can do any computation with better complexity than a Turing machine, save for quantum computing.