Just yesterday [0] I also did an upper bound estimate on computing power of a human brain based on assumption that brains carry out irreversible computations. E.g. inputs of an AND gate can not be recovered from the gate output. This forces increase of entropy. This is known as Landauer's principle or Landauer's limit [1].
The Landauer's limit suggests that a brain consuming 20W at 36C can carry out no more than ~1e22 irreversible operations per second (20W / (309.2K * Boltzmann constant * ln(2))).
That bounds brains at ~1e21 FLOP/s (~10 bits erased per FLOP). The best supercomputer right now does ~4e17 FLOP/s.
That's log2(1e21 / 4e17) ~11 doublings of computing power until supercomputers will be faster than thermodynamic maximum of FLOPS power of brains.
Assuming we keep up the doubling time below 3 years, we will have supercomputers faster than a human brain in up to 3 * 11 ~ 33 years.
And at that rate we will need another log2(1000^3) ~ 30 doublings to reach humanity brains computational power, so up to another 90 years.
Overall, I don't see a reason why not to use biological platform for general type computations. If we are able to grow muscle tissue in a lab on an industrial scale, then we should be able to learn how to grow neurons in a lab on an industrial scale. Apparently neurons are a lot more difficult to grow, but it's still perfectly doable [2]. The issue is that we don't know how to grow them so that they do useful computation. But I can easily imagine that AWS and competition will be selling access to teachable biological neurons in the mid term future e.g. in 30 years.
[0] https://news.ycombinator.com/item?id=26623730
[1] https://en.wikipedia.org/wiki/Landauer%27s_principle
[2] https://www.youtube.com/watch?v=V2YDApNRK3g