Reason behind using inducible promoter for heterologous expression
Heterologous promoters often express genes that are toxic to the organism when expressed in too high quantities. When the genes are expressed constitutively, the organism will either grow slowly or die before they reach a high density suitable for production of the protein. 

As such, it is not about expressing the genes all the time, but expressing the maximum amount of gene product over the shortest period of time. It doesn't make sense for the cells to express the gene product all the time, if they can't reach sufficient densities first. More product will be made if the cells are allowed to grow to a relatively high density, then inducing expression on all of them. This would allow relatively large production levels in a short period of time.