First a possible language thing:
If by "testing" you mean "verification" there are safety critical applications where it is applicable, however, not as often as some of those from the olden days of failing electronics believe it is needed elsewhere.
If by "testing" you mean "aid in hardware repair" there should be no applications.

What are you making? If it is not extremely safety critical, I would consider your proposal a waste of effort. The failure of electronic components in a well designed system is so infinitessimally small that a hardware failure occur too rarely to make the cost of the added components, time and effort have an even moderate rate of return.

So where are we? If you make something safety critical, you MUST make a well designed system and add some verification circuitry. If you make something that is not safety critical, you SHOULD make a well designed system and verification circuitry will not be needed.

Erik