1) Humans can estimate their own uncertainty. Ask a person to show how long a meter is, and they'll give you an estimate. Then ask them to show you the "error bounds", i.e. what they're "quite certain" the meter is longer than and shorter than. You are likely to get sensible bounds. Now, humans aren't amazing at this, but the brain does have capacity for estimating how uncertain it is.
2) No, you don't really trust humans. This very fact that humans are often imperfect in estimating their own uncertainty makes us very stupid sometimes. How many times you were sure you know something for a fact, for it to turn out to be completely false. This is why society tries to not put too much responsibility into the hands of a single person, or at least to provide help and/or safety mechanisms if that is the case.
Ask a programmer to estimate how long it'll take them to code something to see if we really have error bars on complex functions. The margin will be so wide as to be completely useless.
We do have error bars on simple measurements already. They're right there in the data sheet for the sensor. What you're asking for are error bars on things several levels distant in the layers of abstraction. Humans suck at that. We only cope the same way machines do: through constant negative feedback.
Programmers can give you good error bounds. Ask what the best and worst case is for solving a problem, and 80% of the time they will be within those bounds.
The problem is that management doesn't want to hear about the worst case, because it looks bad for them politically.
1) Humans can estimate their own uncertainty. Ask a person to show how long a meter is, and they'll give you an estimate. Then ask them to show you the "error bounds", i.e. what they're "quite certain" the meter is longer than and shorter than. You are likely to get sensible bounds. Now, humans aren't amazing at this, but the brain does have capacity for estimating how uncertain it is.
2) No, you don't really trust humans. This very fact that humans are often imperfect in estimating their own uncertainty makes us very stupid sometimes. How many times you were sure you know something for a fact, for it to turn out to be completely false. This is why society tries to not put too much responsibility into the hands of a single person, or at least to provide help and/or safety mechanisms if that is the case.