Most Republicans, and probably most people in general, think that unemployed workers provide no value to anyone. Many, including most Republicans, believe that unemployment assistance and welfare are wasteful handouts that encourage people to remain without work.
There is a flip side to examine:
When people decry the actions of the Federal Reserve they mention one particular bad scenario - inflation.
The Federal Reserve has two mandates - stable prices and full employment. Why do many conservatives fixate on stable prices versus full employment?
Unemployed workers are willing to take a particular job at a lower wage than they would if they already had a job. The presence of unemployed workers exerts downward pressure on the wages of many of those currently employed. There is a trickle-up effect on this downward pressure and works its way nearly up to median income levels.
Who benefits from lower wages? Employers and business owners. Think of industries that are dependent on low wage workers, and have consumers that are price sensitive. Imagine the impact of increasing worker wages. At worst, possibly going out of business, at best reduced profits. Now imagine the effect of decreasing real (inflation adjusted) wages. Increased profits, and the ability to treat workers as poorly as you want.
Investors have reaped massive gains over the past nearly 5 years, however workers have not. The wages of the top 5% of workers have risen far faster than the rest of the country over the last 25 years.
Downward pressure on wages, coming from the bottom, hurts low to mid wage workers, but helps some of the highest earners, at least in the short term. In the long-term, the overall economy suffers as people drop out of the workforce and their skills fade. It also hurts businesses' customer-bases, but that is a slower erosion, and one that is reduced through things like unemployment and welfare.
Focusing on inflation, and implicitly promoting higher unemployment provides some with short-term gains, at the expense of the long term health of the economy, and the bottom half of workers.