Firstly, examine the downsides of too little unemployment: When too many resources of labour are put for one job, each next addition of employee causes a decrease in the productivity, due to the diminishing marginal returns
Low unemployment can also cause inflation. Less unemployed people means less people to hire from, thus employers are forced to increase wages to attract and hold talent. Firms may try to outweigh the increase in wages by increasing the prices of goods and services. This leads to inflation. Additionally, the increase in wages for workers means that there is more money to be spent. The higher demand causes further increase in prices. As demand for goods and services outpaces the economy’s ability to supply them, prices can rise.
For other smaller firms, the higher wage demanded by workers can restrain firms from hiring qualified or talented workers. This again decreases efficiency.