They sound like interesting tools, especially since there are some sorts of problems where small amounts of unpredictable error can be helpful, like repetitive Monte Carlo-style simulations.
But it also seems like an intimidatingly large area to start learning about.
https://en.wikipedia.org/wiki/MONIAC http://www.analogmuseum.org/english/introduction/
I suspect you're already aware of this, but nonetheless - asynchronous digital logic (ie no clock) does exist! I've never had the chance to play with it though.
Digital systems are almost exclusively a pairing of combinational logic with digital "checkpointing" or pipelining.
With that in mind, in digital systems, as the clock speed increases the difference between combinational and sequential logic drops. Analog provides yet another layer of computational capability on top of that.
Analog computers can perform dramatically more complex work, faster, and with a fraction of the resources -- at the cost of accuracy. The brain is able to consolidate and handle various analog processes to generate what we perceive as the "work product."
Re: 200Hz, it's unlikely the brain operates synchronously so it's unlikely to have an operating frequency of any rate let alone 200Hz. There are of course local systemic limitations such as the refresh rate of the eye. That's more the frequency defined by the "capacitive" capability of the retina.
A refresh rate in a digital system is global: the clock is the source of truth and great pains are taken to ensure clock skew (the difference in time between when the clock edge rises at one end of the wire vs the other) is within a tightly bounded range to ensure coherence of the overall system. An analog combinational computer would just do its work as the data arrives -- not at the rising or falling edge of some 200Hz signal subject to physiological limitations.