Nature is good reference point but it's not by any means optimal. One example may be human eye - we can make cameras orders of magnitude better than eyes created by evolution.
You can look at it the other way around - dopamine and other neuro transmitters as poor approximation of backpropagation. It has many flaws for example tight harmful loops ie. addictions.
Majority of brain work is ignoring irrelevant information (attention) and small scale hallucinations (we don't see world as is but slightly hallucinated to keep it stable - ie. they way brain processes blinking <<turns off>>, you can peek at those nuances with ie. optical illusions etc).
One of missing bits in neural nets may be reusing its output as input (embedded in inference itself, not poor mans re-prompting).
Once it's sorted out I'd argue the performance will skyrocket and give opportunity to massive optimisations ie. embedding things like known functions - imagine brain which has known, very narrowed, available functions at its disposal - all mathematical functions on numbers, logic, optimal sorting etc. Imagine if as thinking human you'd have access to accurate functions - the sky is a limit.