If we are to regard any human activity as being too important to have to rely on the market, then, surely, those tasks the performance of which is essential to life itself ought to be the ones.

That is true, but there's more than one way to skin a cat. Any product that we all need can be funded by all of us through any means, not just via the employment channel. We can "underpay" essential workers if we, in Congress assembled, subsidize them with a stipend paid by us as taxpayers (but not necessarily by raising taxes, because a UBI may not be inflationary) rather than as consumers. Rather than let politicians decide what products be subsidized, we can use a taxable UBI.

I don't believe that a UBI will produce so many otherwise starving artists that the job market will suffer. Precious few people will actually drop out to live on, say, 12k per year.

The UBI is essentially a technology of demand, a way to give more people access to more outputs at a time when the technologies of supply (globalization and automation) are reducing the marginal costs of goods and services. To the extent a UBI creates demand and results in more people having more access to necessities, it's a better paradigm than "you-eat-what-you-kill."