What if all failures occurred truly randomly? Well, for one thing the math would be easier.

The exponential distribution would be the only time to failure distribution—we wouldn’t need Weibull or other complex multi-parameter models. Knowing the failure rate for an hour would be all we would need to know, over any time frame.

Sample size and test planning would be simpler. Just run the samples at hand long enough to accumulate enough hours to provide a reasonable estimate for the failure rate.

Would the design process change?

Yes, I suppose it would. The effects of early life and wear-out would not exist. Once a product is placed into service, the chance to fail the first hour would be the same as in any hour of its operation. It would fail eventually, and the chance of failing before a year would solely depend on the chance of failure per hour.

A higher failure rate would suggest it would have a lower chance of surviving very long. 

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