The demand for unskilled, low pay labour would be fairly inelastic if per-worker productivity was fixed, because these wages are set by a bargain between the employers and the workers where the employers have the majority of bargaining power.

If per-worker productivity can significantly increased by investing in optimization and automation, then yes, demand for labour becomes more flexible, and increases in labour costs would create more unemployment.

It seems to me that the gains in general efficiency of the economy would compensate for the extra costs of unemployment benefits to more people. After all, the government could always increase corporate taxes to gather the money it need to pay benefits.

In principle it is possible to imagine an hypothetical (utopian? dystopian?) future where the vast majority of people are unemployed and live on unemployment benefits, while the few people who earn an income from a job or investment pay all the taxes.
I haven't considered this scenario in enough detail to say that this scenario would be likely or desirable, but it does seem like an intuitively plausible high-automation scenario.