It's the lack of full-scale, realistic tests of complete systems that cause problems. There's just not the money for it nowadays. For example, Orion's crew vehicle had budgeted 2 aeroplane parachute drop tests. Apollo's landing module had over 230. Interestingly, they recorded anomalies on over 210 of those.I would argue that modern designs that learn from the mistakes of past designs require less testing. Maybe it takes 230 drops to understand the aerodynamics of a falling capsule, but once the knowledge is obtained, it only takes 2 to verify a new capsule works as good as the old one.
As for simulations, well one of the catch-phrases in the rocket engine business is 'plumbing never leaks in simulations'.
So why not simulate leaky plumbing? Computer modeling has come a very long way over time.
'You ain't tested it till you've tested it', he said.... The space of possible failures rises exponentially with the number of parts, when you consider all the ways they can interact.
True, but each new failure requires a series of events more complex than previous failures. You're using a bunch of examples of old failures to imply that new designs will fail in the same way, when the reality is that new designs have the benefit of learning from every single previous failure, and every subsequent failure further increases the reliability of the system.
I'm reminded of Asimov's essay, The Relativity of Wrong[0]. Despite your experience in the field, it seems you're too eager to assume that every new idea can be just as wrong as the previous one. Sure, new space vehicle designs like those from SpaceX may fail in ways we couldn't predict, but that is completely different from saying that they'll be less safe or less reliable than their predecessors, or that they have to fail in all the same ways as their predecessors first in order to prove their success.
[0] http://chem.tufts.edu/AnswersInScience/RelativityofWrong.htm