This is slightly off topic. Work is rather a vague term. If you break it down into it's components: effort, compensation, social-benefit, etc. then you can start to assign relative merit to different kinds of work. For example financiers which might be categorised as: high compensation, low to moderate effort and low social benefit and janitors: low compensation, moderate effort, low compensation. Now you can start to make value judgements about how different types of work are rated or (should be) valued by the general public or society as a whole. You can also factor out the ideological or moral components attributed to work by various political factions and start to answer interesting questions such how much should teachers be paid and what jobs which are low compensation, low social benefit should we be automating as fast as possible.
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.
