> I would posit that Distributed systems are typically a category of concurrent systems
Absolutely, and so are interactive systems, which are distributed/concurrent between the computer and the human user. In TLA+ all of these are described in the same way, but colloquially, engineers think of them differently, and there are actually good reasons for that, too. E.g. virtually no concurrent algorithms (for a single computer) account for a failure of a single core and its associated L1 cache, but all distributed algorithms do.
Yep, and a good example is when TLA+ was used against some AWS services [0], it was able to expose bugs that were 35 states deep. To be able to find such a bug in production would require very good tracing most likely; to have a specification detect such bugs before you have even coded the thing is invaluable.
> 2. distributed systems and concurrency are a very common example of subtle algorithms that engineers often encounter and are tricky to get right without help.
I would posit that Distributed systems are typically a category of concurrent systems; just at a different level of abstraction (threads vs nodes)
[0] - https://en.wikipedia.org/wiki/TLA%2B#Industry_use