What is the consequence of over using a component on a production line?

Quality will be tampered with, eg if you over use a mould without servicing, you will develop issues of inconsistency in weights and dimensions hence affecting quality of output

It depends on what "component" in what "production line" and what is the nature of this production line we are talking about.

1. The general understanding about production line is that it is "continuous process" with raw material(s) flowing from one end, and get processes by different physical/chemical/heat treatments to turn from one shape into other which could be final product or semi-final product, as in the case of chemicals, petrochemicals, ...
2. However, there are also "discrete process" production lines as in manufacturing where discrete components get assembled in a production  line to produce the final or semi-final product.  Take electrical, electronics, mechanical, car industries as examples

Using a component in such a production line (case2) seems to be quite natural ...

While using it in the continuous process production line needs to be explained and justified !