If you allow competition the market will do this. Compensation also takes into account the joy the job provides, some jobs are relatively pleasant and thus pay less than some that are much worse.
As for automation, I completely disagree - we automate where we can get the biggest gain on output. So if something costs a lot or has high social benefit we should automate it as much as possible so that it can provide more benefits to more people.
There are many types of job where market forces cannot solve the problem. (Within the context of the Universal Basic Income) there may entire categories of types of job that could be created to solve social (in the most general sense) or civic problems. For example charitable or education related activities are low to no profit - or at least it is not easy to measure their benefit directly or immediately, but high social value in the sense that they mitigate future problem that result in increase expenditures or taxes and so have long term value. Since the market uses money and direct profit as a means to measure everything it simply cannot deal with this.
Two examples that invalidate your last sentence would be Khan Academy and Mozilla -- both very competitive places to get a job, yet they don't pay substantially above market; their mission is what draws employees in. Not all competitive forces are financial in nature.
We could argue about the extent to which these nonfinancial competitive forces influence (or ought to influence) the market, but saying that they "simply cannot" seems false.
Compensation also takes into account the joy the job provides, some jobs are relatively pleasant and thus pay less than some that are much worse.
That's not generally my observation of the world. No-skill-required jobs pay less, skill-required jobs pay more. There's a slight bonus for dangerous jobs, but not a heap, relatively speaking. Pleasure derived or not only appears to have an effect on income levels outside of traditional employment and into freelancing territory, for example with starving artists and writers.
As for automation, I completely disagree - we automate where we can get the biggest gain on output. So if something costs a lot or has high social benefit we should automate it as much as possible so that it can provide more benefits to more people.