Can you point to specific cases where having a second legislative house, wherein representatives of 14% of the population (the 20 least populous states) can stop any action whatsoever from being taken has actually had a use?

It's rather difficult to find good examples. News coverage of bills that don't pass is much harder to find. There's an additional complication in that any given case where I think it was a fantastic thing that a bill didn't pass is as likely to be interpreted by someone else as a damn shame.

I'm also fairly sure that it's a poorly designed system and its best defense is status quo bias rather than effective governance.

I agree it's a poorly designed system. There absolutely are better ways of doing things. But I don't know entirely which they are, and there are far more ways of making the system worse than better. I'm just not convinced that abolishing is necessarily an improvement.

It's hard to design well-functioning political systems. Just as it's hard to design any complicated interacting system with many parts. Note too that the system is not just the formal rules, either, but includes the traditions about what is acceptable. These evolved in tandem. As an example of what can happen when they don't, many Latin American countries borrowed heavily from the formal structure of the U.S. and then promptly slid into dictatorships.

There's a computer programming adage that any complex working system was created by evolving a less-complex working system, rather than writing from scratch. I'd rather see incremental reform than large changes, barring an absolute necessity. Most of what the U.S. Congress does is not terribly time sensitive. It just doesn't matter if most legislative tweaks get passed this month, or even this year. The budget is admittedly a very important exception.

(I too am from California, though I don't currently live there. And yeah, the overrepresentation of "flyover country" is annoying. I would prefer the second chamber to be allocated differently than it currently is, but I still think two chambers is better than one, if for nothing else than slightly reducing groupthink.)